SlideShare a Scribd company logo
Derivatives
Submitted To: Ma’m Sapna Makhdoom
Submitted By:
•Irum GulBahar 02
•Hajrah Majeed 14
•Humera Yousaf 19
•Amna Ayub 21
Topic: Derivatives
Session: 2013-17
Department: Mathematics
Mirpur University Of Science & Technology
(MUST)
• Dedication:
We dedicate this project named “ Derivatives”
to our parents and Family members.
• Abstract
In this project we have discussed about
Derivatives such as Definition , History, Real
life applications, and Application of
derivatives in different sciences.
• Acknowledgement
First of all we would like to thank Allah almighty
for making this project possible for us. Then
special thanks to Ma’m Sapna Makhdoom for
helping us in completing this project
Contents:
1. Definition of Derivative
2. History
3. Real life Applications
4. Applications in Sciences
Definition of Derivative:
1. The Derivative is the exact rate at
which one quantity changes with respect
to another.
2. Geometrically, the derivative is the
slope of curve at the point on the curve.
3. The derivative is often called the
“instantaneous “ rate of change.
4. The derivative of a function represents
an infinitely small change the function
with respect to one of its variables.
• The Process of finding the derivative is called
“differentiation.”
History:
• Modern differentiation and derivatives are usually cradited to “Isaac
Newton” and “Gottfried Leibniz”.
• They developed the fundamental theorem of calculus in the 17th
century. This related differentiation and integration in ways which
revolutionized the methods for computing areas and volumes.
• However , Newton’s work would not have been possible without the
efforts of Isaac Borrow who began early development of the derivative in
the 16th century.
Real life Applications of
Derivatives
Automobiles
• In an automobile there is always an odometer and a
speedometer. These two gauges work in tandem and
allow the driver to determine his speed and his
distance that he has traveled. Electronic versions of
these gauges simply use derivatives to transform the
data sent to the electronic motherboard from the tires
to miles per Hour(MPH) and distance(KM).
Radar Guns
• Keeping with the automobile theme from the previous slide ,
all police officers who use radar guns are actually taking
advantage of the easy use of derivatives. When a radar gun is
pointed and fired at your care on the highway. The gun is able
to determine the time and distance at which the radar was able
to hit a certain section of your vehicle. With the use of
derivative it is able to calculate the speed at which the car was
going and also report the distance that the car was from the
radar gun.
Business
• In the business world there are many applications for
derivatives. One of the most important application is
when the data has been charted on graph or data table
such as excel. Once it has been input, the data can be
graphed and with the applications of derivatives you
can estimate the profit and loss point for certain
ventures.
Graphs:
• The most common application of derivative is to analyze
graphs of data that can be calculated from many different
fields. Using derivative one is able to calculate the gradient at
any point of a graph.
Applications of Derivatives in Various
fields/Sciences:
Such as in:
–Physics
–Biology
–Economics
–Chemistry
–Mathematics
–Others(Psychology,
sociology & geology)
Derivatives in Physics
• In physics, the derivative of the
displacement of a moving body with
respect to time is the velocity of the
body, and the derivative of velocity
W.R.T time is acceleration.
• Newton’s second law of motion states
that the derivative of the momentum
of a body equals the force applied to
the body.
Derivatives in Biology
• Population growth is another instance of
the derivative used in the sciences.
• Suppose n=f(t) is the number of
individuals in some animal or plant
population at time t. the change in the
population size between time t1 and t2
∆n=f(t2)-f(t1).
• The average rate of growth is then is:
Average rate of growth is = (∆n/
∆t)=(f(t2)-f(t1))/(t2-t1)
• The instantaneous rate of growth is the
derivative of the function n with respect
to t, i.e.
growth rate=lim(∆t→0) (∆n/ ∆t)=(dn/dt)
Derivatives in Biology:
• The instantaneous rate of change does not make exact
sense in the previous example because the change in
population is not exactly a continuous process.
However, for large population we can approximate
the population function by a smooth(continuous)
curve.
– Example: Suppose that a population of bacteria doubles its
population , n, every hour. Denote by n0 the initial
population i.e. n(0)=n0. In general then,
n(t)=2t no
– Thus the rate of growth of the population at time t is
(dn/dt)=no2tln2
Derivatives in Economics:
• Use of derivatives in Economics is as follows:
• Let x represent the number of units of a certain commodity produced
by some company. Denote by C(x) the cost the company incurs in
producing x units. Then the derivative of C(x) is what’s called the
marginal cost:
Marginal cost =(dC/dx)
• Furthermore, suppose the company knows that if it produces x units,
they can expect the revenue to be R(x),i.e. the revenue is a function of
the number of units produced. Then the derivative of R(x) is what’s
called the marginal revenue.
Marginal revenue= (dR/dx)
• If x units are sold, then total profit is given by the formula:
P(x)=R(x)-C(x)
• The derivative of profit function is the marginal profit:
Marginal profit=(dP/dx)= (dR/dx)-(dC/dx).
Derivatives in Chemistry
• One use of derivatives in chemistry is
when you want to find the
concentration of an element in a
product.
• Derivative is used to calculate rate of
reaction and compressibility in
chemistry.
Derivatives in Mathematics:
The most common use of the derivatives
in Mathematics is to study functions
such as:
• Extreme values of function
• The Mean Value theorem
• Monotonic functions
• Concavity & curve sketching
• Newton’s Method etc.
Connecting Derivatives
Derivatives
Continuity
Inflection
Points
Motion
Problems
Vectors
Mean
Value
Theorem
Implicit
Function
Theorem
Estimating
Graphs
Some other Applications of
Derivatives
• Derivatives are also use to
calculate:
1. Rate of heat flow in Geology.
2. Rate of improvement of
performance in psychology
3. Rate of the spread of a rumor in
sociology.
Conclusion:
• Derivatives are constantly used in
everyday life to help measure how
much something is changing. They're
used by the government in population
censuses, various types of sciences,
and even in economics. Knowing how
to use derivatives, when to use them,
and how to apply them in everyday
life can be a crucial part of any
profession, so learning early is always
a good thing.
Applications of Derivatives

More Related Content

What's hot

A presentation on differencial calculus
A presentation on differencial calculusA presentation on differencial calculus
A presentation on differencial calculus
bujh balok
 
Applications of Integrations
Applications of IntegrationsApplications of Integrations
Applications of Integrations
itutor
 
Continuity and differentiability
Continuity and differentiability Continuity and differentiability
Continuity and differentiability
Seyid Kadher
 
Derivatives and their Applications
Derivatives and their ApplicationsDerivatives and their Applications
Derivatives and their Applications
usmancp2611
 
Application of derivatives
Application of derivatives Application of derivatives
Application of derivatives
Seyid Kadher
 
Differential calculus
Differential calculusDifferential calculus
Differential calculus
Shubham .
 
Maxima and minima
Maxima and minimaMaxima and minima
Maxima and minima
Umesh Pandey
 
Integrals and its applications
Integrals  and  its applicationsIntegrals  and  its applications
Integrals and its applications
Poojith Chowdhary
 
The Application of Derivatives
The Application of DerivativesThe Application of Derivatives
The Application of Derivatives
divaprincess09
 
Integration
IntegrationIntegration
Integration
Chhitiz Shrestha
 
Real Life Application of Vector
Real Life Application of VectorReal Life Application of Vector
Real Life Application of Vector
Iftekhar Bhuiyan
 
Real life application of Function.
Real life application of Function.Real life application of Function.
Real life application of Function.
Jholok Biswash
 
Differentiation
DifferentiationDifferentiation
Differentiation
Vivek Jain
 
Application of derivatives 2 maxima and minima
Application of derivatives 2  maxima and minimaApplication of derivatives 2  maxima and minima
Application of derivatives 2 maxima and minima
sudersana viswanathan
 
Benginning Calculus Lecture notes 2 - limits and continuity
Benginning Calculus Lecture notes 2 - limits and continuityBenginning Calculus Lecture notes 2 - limits and continuity
Benginning Calculus Lecture notes 2 - limits and continuity
basyirstar
 
Rules of derivative
Rules of derivativeRules of derivative
Rules of derivative
jameel shigri
 
MEAN VALUE THEOREM
MEAN VALUE THEOREMMEAN VALUE THEOREM
Basic Calculus 11 - Derivatives and Differentiation Rules
Basic Calculus 11 - Derivatives and Differentiation RulesBasic Calculus 11 - Derivatives and Differentiation Rules
Basic Calculus 11 - Derivatives and Differentiation Rules
Juan Miguel Palero
 
Laplace Transformation & Its Application
Laplace Transformation & Its ApplicationLaplace Transformation & Its Application
Laplace Transformation & Its Application
Chandra Kundu
 
Complex Numbers
Complex NumbersComplex Numbers
Complex Numbers
itutor
 

What's hot (20)

A presentation on differencial calculus
A presentation on differencial calculusA presentation on differencial calculus
A presentation on differencial calculus
 
Applications of Integrations
Applications of IntegrationsApplications of Integrations
Applications of Integrations
 
Continuity and differentiability
Continuity and differentiability Continuity and differentiability
Continuity and differentiability
 
Derivatives and their Applications
Derivatives and their ApplicationsDerivatives and their Applications
Derivatives and their Applications
 
Application of derivatives
Application of derivatives Application of derivatives
Application of derivatives
 
Differential calculus
Differential calculusDifferential calculus
Differential calculus
 
Maxima and minima
Maxima and minimaMaxima and minima
Maxima and minima
 
Integrals and its applications
Integrals  and  its applicationsIntegrals  and  its applications
Integrals and its applications
 
The Application of Derivatives
The Application of DerivativesThe Application of Derivatives
The Application of Derivatives
 
Integration
IntegrationIntegration
Integration
 
Real Life Application of Vector
Real Life Application of VectorReal Life Application of Vector
Real Life Application of Vector
 
Real life application of Function.
Real life application of Function.Real life application of Function.
Real life application of Function.
 
Differentiation
DifferentiationDifferentiation
Differentiation
 
Application of derivatives 2 maxima and minima
Application of derivatives 2  maxima and minimaApplication of derivatives 2  maxima and minima
Application of derivatives 2 maxima and minima
 
Benginning Calculus Lecture notes 2 - limits and continuity
Benginning Calculus Lecture notes 2 - limits and continuityBenginning Calculus Lecture notes 2 - limits and continuity
Benginning Calculus Lecture notes 2 - limits and continuity
 
Rules of derivative
Rules of derivativeRules of derivative
Rules of derivative
 
MEAN VALUE THEOREM
MEAN VALUE THEOREMMEAN VALUE THEOREM
MEAN VALUE THEOREM
 
Basic Calculus 11 - Derivatives and Differentiation Rules
Basic Calculus 11 - Derivatives and Differentiation RulesBasic Calculus 11 - Derivatives and Differentiation Rules
Basic Calculus 11 - Derivatives and Differentiation Rules
 
Laplace Transformation & Its Application
Laplace Transformation & Its ApplicationLaplace Transformation & Its Application
Laplace Transformation & Its Application
 
Complex Numbers
Complex NumbersComplex Numbers
Complex Numbers
 

Similar to Applications of Derivatives

differentiation (1).pptx
differentiation (1).pptxdifferentiation (1).pptx
differentiation (1).pptx
Alpa Rajput
 
Mathematician inretgrals.pdf
Mathematician inretgrals.pdfMathematician inretgrals.pdf
Mathematician inretgrals.pdf
AlwandBarzani
 
Applications Of Math In Real Life And Business
Applications Of Math In Real Life And BusinessApplications Of Math In Real Life And Business
Applications Of Math In Real Life And Business
Muhammad Ahmad Badar
 
Maths Investigatory Project Class 12 on Differentiation
Maths Investigatory Project Class 12 on DifferentiationMaths Investigatory Project Class 12 on Differentiation
Maths Investigatory Project Class 12 on Differentiation
SayanMandal31
 
Finding the Extreme Values with some Application of Derivatives
Finding the Extreme Values with some Application of DerivativesFinding the Extreme Values with some Application of Derivatives
Finding the Extreme Values with some Application of Derivatives
ijtsrd
 
Emm3104 chapter 1 part2
Emm3104 chapter 1 part2Emm3104 chapter 1 part2
Emm3104 chapter 1 part2
Khairiyah Sulaiman
 
Intro diffcall3b
Intro diffcall3bIntro diffcall3b
Intro diffcall3b
sheetslibrary
 
At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docx
At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docxAt a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docx
At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docx
ikirkton
 
Caculus
CaculusCaculus
Caculus.pptx
Caculus.pptxCaculus.pptx
Caculus.pptx
Er. Rahul Jarariya
 
Calculus
CalculusCalculus
Mathematical modelling and its application in weather forecasting
Mathematical modelling and its application in weather forecastingMathematical modelling and its application in weather forecasting
Mathematical modelling and its application in weather forecasting
Sarwar Azad
 
maths.ppt
maths.pptmaths.ppt
maths.ppt
Ajay Singh
 
Lecture_2_Stats.pdf
Lecture_2_Stats.pdfLecture_2_Stats.pdf
Lecture_2_Stats.pdf
paijitk
 
ITS for Crowds
ITS for CrowdsITS for Crowds
ITS for Crowds
Serge Hoogendoorn
 
Ch 3 the derivative
Ch 3 the derivativeCh 3 the derivative
Ch 3 the derivative
FuaadAbdirizakElmi1
 
Application of differentiation
Application   of   differentiationApplication   of   differentiation
Application of differentiation
Dhanush Kumar
 
CS3114_09212011.ppt
CS3114_09212011.pptCS3114_09212011.ppt
CS3114_09212011.ppt
Arumugam90
 
Mathematical modeling
Mathematical modelingMathematical modeling
Mathematical modeling
Dr. Deepak Kumar
 
NUMERICAL ANALYSIS TO OPTIMIZE THE HEAT TRANSFER RATE OF TUBE-IN-TUBE HELICAL...
NUMERICAL ANALYSIS TO OPTIMIZE THE HEAT TRANSFER RATE OF TUBE-IN-TUBE HELICAL...NUMERICAL ANALYSIS TO OPTIMIZE THE HEAT TRANSFER RATE OF TUBE-IN-TUBE HELICAL...
NUMERICAL ANALYSIS TO OPTIMIZE THE HEAT TRANSFER RATE OF TUBE-IN-TUBE HELICAL...
Netha Jashuva
 

Similar to Applications of Derivatives (20)

differentiation (1).pptx
differentiation (1).pptxdifferentiation (1).pptx
differentiation (1).pptx
 
Mathematician inretgrals.pdf
Mathematician inretgrals.pdfMathematician inretgrals.pdf
Mathematician inretgrals.pdf
 
Applications Of Math In Real Life And Business
Applications Of Math In Real Life And BusinessApplications Of Math In Real Life And Business
Applications Of Math In Real Life And Business
 
Maths Investigatory Project Class 12 on Differentiation
Maths Investigatory Project Class 12 on DifferentiationMaths Investigatory Project Class 12 on Differentiation
Maths Investigatory Project Class 12 on Differentiation
 
Finding the Extreme Values with some Application of Derivatives
Finding the Extreme Values with some Application of DerivativesFinding the Extreme Values with some Application of Derivatives
Finding the Extreme Values with some Application of Derivatives
 
Emm3104 chapter 1 part2
Emm3104 chapter 1 part2Emm3104 chapter 1 part2
Emm3104 chapter 1 part2
 
Intro diffcall3b
Intro diffcall3bIntro diffcall3b
Intro diffcall3b
 
At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docx
At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docxAt a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docx
At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docx
 
Caculus
CaculusCaculus
Caculus
 
Caculus.pptx
Caculus.pptxCaculus.pptx
Caculus.pptx
 
Calculus
CalculusCalculus
Calculus
 
Mathematical modelling and its application in weather forecasting
Mathematical modelling and its application in weather forecastingMathematical modelling and its application in weather forecasting
Mathematical modelling and its application in weather forecasting
 
maths.ppt
maths.pptmaths.ppt
maths.ppt
 
Lecture_2_Stats.pdf
Lecture_2_Stats.pdfLecture_2_Stats.pdf
Lecture_2_Stats.pdf
 
ITS for Crowds
ITS for CrowdsITS for Crowds
ITS for Crowds
 
Ch 3 the derivative
Ch 3 the derivativeCh 3 the derivative
Ch 3 the derivative
 
Application of differentiation
Application   of   differentiationApplication   of   differentiation
Application of differentiation
 
CS3114_09212011.ppt
CS3114_09212011.pptCS3114_09212011.ppt
CS3114_09212011.ppt
 
Mathematical modeling
Mathematical modelingMathematical modeling
Mathematical modeling
 
NUMERICAL ANALYSIS TO OPTIMIZE THE HEAT TRANSFER RATE OF TUBE-IN-TUBE HELICAL...
NUMERICAL ANALYSIS TO OPTIMIZE THE HEAT TRANSFER RATE OF TUBE-IN-TUBE HELICAL...NUMERICAL ANALYSIS TO OPTIMIZE THE HEAT TRANSFER RATE OF TUBE-IN-TUBE HELICAL...
NUMERICAL ANALYSIS TO OPTIMIZE THE HEAT TRANSFER RATE OF TUBE-IN-TUBE HELICAL...
 

Recently uploaded

Juneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School DistrictJuneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School District
David Douglas School District
 
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
indexPub
 
Temple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation resultsTemple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation results
Krassimira Luka
 
Bonku-Babus-Friend by Sathyajith Ray (9)
Bonku-Babus-Friend by Sathyajith Ray  (9)Bonku-Babus-Friend by Sathyajith Ray  (9)
Bonku-Babus-Friend by Sathyajith Ray (9)
nitinpv4ai
 
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
ImMuslim
 
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
TechSoup
 
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdfREASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
giancarloi8888
 
The basics of sentences session 7pptx.pptx
The basics of sentences session 7pptx.pptxThe basics of sentences session 7pptx.pptx
The basics of sentences session 7pptx.pptx
heathfieldcps1
 
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptxBIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
RidwanHassanYusuf
 
How Barcodes Can Be Leveraged Within Odoo 17
How Barcodes Can Be Leveraged Within Odoo 17How Barcodes Can Be Leveraged Within Odoo 17
How Barcodes Can Be Leveraged Within Odoo 17
Celine George
 
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit InnovationLeveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
TechSoup
 
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
Level 3 NCEA - NZ: A  Nation In the Making 1872 - 1900 SML.pptLevel 3 NCEA - NZ: A  Nation In the Making 1872 - 1900 SML.ppt
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
Henry Hollis
 
Pharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brubPharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brub
danielkiash986
 
CIS 4200-02 Group 1 Final Project Report (1).pdf
CIS 4200-02 Group 1 Final Project Report (1).pdfCIS 4200-02 Group 1 Final Project Report (1).pdf
CIS 4200-02 Group 1 Final Project Report (1).pdf
blueshagoo1
 
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
Nguyen Thanh Tu Collection
 
SWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptxSWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptx
zuzanka
 
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem studentsRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Himanshu Rai
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
Jyoti Chand
 
Electric Fetus - Record Store Scavenger Hunt
Electric Fetus - Record Store Scavenger HuntElectric Fetus - Record Store Scavenger Hunt
Electric Fetus - Record Store Scavenger Hunt
RamseyBerglund
 
Benner "Expanding Pathways to Publishing Careers"
Benner "Expanding Pathways to Publishing Careers"Benner "Expanding Pathways to Publishing Careers"
Benner "Expanding Pathways to Publishing Careers"
National Information Standards Organization (NISO)
 

Recently uploaded (20)

Juneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School DistrictJuneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School District
 
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
 
Temple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation resultsTemple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation results
 
Bonku-Babus-Friend by Sathyajith Ray (9)
Bonku-Babus-Friend by Sathyajith Ray  (9)Bonku-Babus-Friend by Sathyajith Ray  (9)
Bonku-Babus-Friend by Sathyajith Ray (9)
 
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
 
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
 
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdfREASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
 
The basics of sentences session 7pptx.pptx
The basics of sentences session 7pptx.pptxThe basics of sentences session 7pptx.pptx
The basics of sentences session 7pptx.pptx
 
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptxBIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
 
How Barcodes Can Be Leveraged Within Odoo 17
How Barcodes Can Be Leveraged Within Odoo 17How Barcodes Can Be Leveraged Within Odoo 17
How Barcodes Can Be Leveraged Within Odoo 17
 
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit InnovationLeveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
 
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
Level 3 NCEA - NZ: A  Nation In the Making 1872 - 1900 SML.pptLevel 3 NCEA - NZ: A  Nation In the Making 1872 - 1900 SML.ppt
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
 
Pharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brubPharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brub
 
CIS 4200-02 Group 1 Final Project Report (1).pdf
CIS 4200-02 Group 1 Final Project Report (1).pdfCIS 4200-02 Group 1 Final Project Report (1).pdf
CIS 4200-02 Group 1 Final Project Report (1).pdf
 
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
 
SWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptxSWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptx
 
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem studentsRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
 
Electric Fetus - Record Store Scavenger Hunt
Electric Fetus - Record Store Scavenger HuntElectric Fetus - Record Store Scavenger Hunt
Electric Fetus - Record Store Scavenger Hunt
 
Benner "Expanding Pathways to Publishing Careers"
Benner "Expanding Pathways to Publishing Careers"Benner "Expanding Pathways to Publishing Careers"
Benner "Expanding Pathways to Publishing Careers"
 

Applications of Derivatives

  • 2. Submitted To: Ma’m Sapna Makhdoom Submitted By: •Irum GulBahar 02 •Hajrah Majeed 14 •Humera Yousaf 19 •Amna Ayub 21 Topic: Derivatives Session: 2013-17 Department: Mathematics Mirpur University Of Science & Technology (MUST)
  • 3.
  • 4. • Dedication: We dedicate this project named “ Derivatives” to our parents and Family members.
  • 5. • Abstract In this project we have discussed about Derivatives such as Definition , History, Real life applications, and Application of derivatives in different sciences.
  • 6. • Acknowledgement First of all we would like to thank Allah almighty for making this project possible for us. Then special thanks to Ma’m Sapna Makhdoom for helping us in completing this project
  • 7. Contents: 1. Definition of Derivative 2. History 3. Real life Applications 4. Applications in Sciences
  • 8. Definition of Derivative: 1. The Derivative is the exact rate at which one quantity changes with respect to another. 2. Geometrically, the derivative is the slope of curve at the point on the curve. 3. The derivative is often called the “instantaneous “ rate of change. 4. The derivative of a function represents an infinitely small change the function with respect to one of its variables. • The Process of finding the derivative is called “differentiation.”
  • 9. History: • Modern differentiation and derivatives are usually cradited to “Isaac Newton” and “Gottfried Leibniz”. • They developed the fundamental theorem of calculus in the 17th century. This related differentiation and integration in ways which revolutionized the methods for computing areas and volumes. • However , Newton’s work would not have been possible without the efforts of Isaac Borrow who began early development of the derivative in the 16th century.
  • 10. Real life Applications of Derivatives
  • 11. Automobiles • In an automobile there is always an odometer and a speedometer. These two gauges work in tandem and allow the driver to determine his speed and his distance that he has traveled. Electronic versions of these gauges simply use derivatives to transform the data sent to the electronic motherboard from the tires to miles per Hour(MPH) and distance(KM).
  • 12. Radar Guns • Keeping with the automobile theme from the previous slide , all police officers who use radar guns are actually taking advantage of the easy use of derivatives. When a radar gun is pointed and fired at your care on the highway. The gun is able to determine the time and distance at which the radar was able to hit a certain section of your vehicle. With the use of derivative it is able to calculate the speed at which the car was going and also report the distance that the car was from the radar gun.
  • 13. Business • In the business world there are many applications for derivatives. One of the most important application is when the data has been charted on graph or data table such as excel. Once it has been input, the data can be graphed and with the applications of derivatives you can estimate the profit and loss point for certain ventures.
  • 14. Graphs: • The most common application of derivative is to analyze graphs of data that can be calculated from many different fields. Using derivative one is able to calculate the gradient at any point of a graph.
  • 15. Applications of Derivatives in Various fields/Sciences: Such as in: –Physics –Biology –Economics –Chemistry –Mathematics –Others(Psychology, sociology & geology)
  • 16. Derivatives in Physics • In physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of velocity W.R.T time is acceleration. • Newton’s second law of motion states that the derivative of the momentum of a body equals the force applied to the body.
  • 17. Derivatives in Biology • Population growth is another instance of the derivative used in the sciences. • Suppose n=f(t) is the number of individuals in some animal or plant population at time t. the change in the population size between time t1 and t2 ∆n=f(t2)-f(t1). • The average rate of growth is then is: Average rate of growth is = (∆n/ ∆t)=(f(t2)-f(t1))/(t2-t1) • The instantaneous rate of growth is the derivative of the function n with respect to t, i.e. growth rate=lim(∆t→0) (∆n/ ∆t)=(dn/dt)
  • 18. Derivatives in Biology: • The instantaneous rate of change does not make exact sense in the previous example because the change in population is not exactly a continuous process. However, for large population we can approximate the population function by a smooth(continuous) curve. – Example: Suppose that a population of bacteria doubles its population , n, every hour. Denote by n0 the initial population i.e. n(0)=n0. In general then, n(t)=2t no – Thus the rate of growth of the population at time t is (dn/dt)=no2tln2
  • 19. Derivatives in Economics: • Use of derivatives in Economics is as follows: • Let x represent the number of units of a certain commodity produced by some company. Denote by C(x) the cost the company incurs in producing x units. Then the derivative of C(x) is what’s called the marginal cost: Marginal cost =(dC/dx) • Furthermore, suppose the company knows that if it produces x units, they can expect the revenue to be R(x),i.e. the revenue is a function of the number of units produced. Then the derivative of R(x) is what’s called the marginal revenue. Marginal revenue= (dR/dx) • If x units are sold, then total profit is given by the formula: P(x)=R(x)-C(x) • The derivative of profit function is the marginal profit: Marginal profit=(dP/dx)= (dR/dx)-(dC/dx).
  • 20. Derivatives in Chemistry • One use of derivatives in chemistry is when you want to find the concentration of an element in a product. • Derivative is used to calculate rate of reaction and compressibility in chemistry.
  • 21. Derivatives in Mathematics: The most common use of the derivatives in Mathematics is to study functions such as: • Extreme values of function • The Mean Value theorem • Monotonic functions • Concavity & curve sketching • Newton’s Method etc.
  • 23. Some other Applications of Derivatives • Derivatives are also use to calculate: 1. Rate of heat flow in Geology. 2. Rate of improvement of performance in psychology 3. Rate of the spread of a rumor in sociology.
  • 24. Conclusion: • Derivatives are constantly used in everyday life to help measure how much something is changing. They're used by the government in population censuses, various types of sciences, and even in economics. Knowing how to use derivatives, when to use them, and how to apply them in everyday life can be a crucial part of any profession, so learning early is always a good thing.