SlideShare a Scribd company logo
1 of 13
Product Rule of Calculus


Or written using the
      “special D” for derivative
             rather than “prime”:
Product Rule of Calculus


For example:
Surface Area
  of a cylinder




I can never remember the formula
The “special d”
also means “boundary”
The “special d”
also means “boundary”
The “special d”
also means “boundary”
The product rule of
  as “derivative”
works also with
  as “boundary”
Volume of a cylinder
Surface area
   of a cylinder
Surface area       Volume
Surface area
   of a cylinder

(top & bottom)   “paper towel roll” side
surface area of a cylinder [∂ Campbell's soup can]

More Related Content

Viewers also liked

Ossiannilsson 131122 trakai_bm
Ossiannilsson 131122 trakai_bmOssiannilsson 131122 trakai_bm
Ossiannilsson 131122 trakai_bmEbba Ossiannilsson
 
Social media adoption: Enterprise-level, worldwide
Social media adoption: Enterprise-level, worldwideSocial media adoption: Enterprise-level, worldwide
Social media adoption: Enterprise-level, worldwideDr. V Vorvoreanu
 
Security Privacy Concerns Third Party APIs
Security Privacy Concerns Third Party APIsSecurity Privacy Concerns Third Party APIs
Security Privacy Concerns Third Party APIsDr. V Vorvoreanu
 
Organisatie ontwerp
Organisatie ontwerpOrganisatie ontwerp
Organisatie ontwerpMark Nijssen
 
Filmand t vbasics1
Filmand t vbasics1Filmand t vbasics1
Filmand t vbasics1NINANC
 
Apop digital media_class 2
Apop digital media_class 2Apop digital media_class 2
Apop digital media_class 2reisa101
 
Ossiannilsson hogskolan dalarna_workshopimpoers_140321
Ossiannilsson hogskolan dalarna_workshopimpoers_140321Ossiannilsson hogskolan dalarna_workshopimpoers_140321
Ossiannilsson hogskolan dalarna_workshopimpoers_140321Ebba Ossiannilsson
 
Presentation1
Presentation1Presentation1
Presentation1slmsaady
 
21st Century Platform From Harrison Spence
21st Century Platform From Harrison Spence21st Century Platform From Harrison Spence
21st Century Platform From Harrison SpenceBrian Spence
 
2010 focus on the short- and long-term effects of ghrelin on energy
2010 focus on the short- and long-term effects of ghrelin on energy2010 focus on the short- and long-term effects of ghrelin on energy
2010 focus on the short- and long-term effects of ghrelin on energyAgrin Life
 
Trabajo realizado para el curso convivencia escolar: prevención en intervenci...
Trabajo realizado para el curso convivencia escolar: prevención en intervenci...Trabajo realizado para el curso convivencia escolar: prevención en intervenci...
Trabajo realizado para el curso convivencia escolar: prevención en intervenci...Piluka Alburquerque
 

Viewers also liked (18)

Ossiannilsson 131122 trakai_bm
Ossiannilsson 131122 trakai_bmOssiannilsson 131122 trakai_bm
Ossiannilsson 131122 trakai_bm
 
Social media adoption: Enterprise-level, worldwide
Social media adoption: Enterprise-level, worldwideSocial media adoption: Enterprise-level, worldwide
Social media adoption: Enterprise-level, worldwide
 
Security Privacy Concerns Third Party APIs
Security Privacy Concerns Third Party APIsSecurity Privacy Concerns Third Party APIs
Security Privacy Concerns Third Party APIs
 
Organisatie ontwerp
Organisatie ontwerpOrganisatie ontwerp
Organisatie ontwerp
 
Jornada Ub 2003
Jornada Ub 2003Jornada Ub 2003
Jornada Ub 2003
 
Filmand t vbasics1
Filmand t vbasics1Filmand t vbasics1
Filmand t vbasics1
 
Augmented reality
Augmented realityAugmented reality
Augmented reality
 
Apop digital media_class 2
Apop digital media_class 2Apop digital media_class 2
Apop digital media_class 2
 
Ossiannilsson hogskolan dalarna_workshopimpoers_140321
Ossiannilsson hogskolan dalarna_workshopimpoers_140321Ossiannilsson hogskolan dalarna_workshopimpoers_140321
Ossiannilsson hogskolan dalarna_workshopimpoers_140321
 
Presentation1
Presentation1Presentation1
Presentation1
 
自動排程
自動排程自動排程
自動排程
 
How Canada Does It
How Canada Does ItHow Canada Does It
How Canada Does It
 
21st Century Platform From Harrison Spence
21st Century Platform From Harrison Spence21st Century Platform From Harrison Spence
21st Century Platform From Harrison Spence
 
Session 01
Session 01Session 01
Session 01
 
2010 focus on the short- and long-term effects of ghrelin on energy
2010 focus on the short- and long-term effects of ghrelin on energy2010 focus on the short- and long-term effects of ghrelin on energy
2010 focus on the short- and long-term effects of ghrelin on energy
 
List kick off lund_5sept2016
List kick off  lund_5sept2016List kick off  lund_5sept2016
List kick off lund_5sept2016
 
Trabajo realizado para el curso convivencia escolar: prevención en intervenci...
Trabajo realizado para el curso convivencia escolar: prevención en intervenci...Trabajo realizado para el curso convivencia escolar: prevención en intervenci...
Trabajo realizado para el curso convivencia escolar: prevención en intervenci...
 
Nu oer
Nu oerNu oer
Nu oer
 

More from Chris Waggoner

Visualizing Higher dimensions
Visualizing Higher dimensionsVisualizing Higher dimensions
Visualizing Higher dimensionsChris Waggoner
 
A3d3ffefe720fd771feb02374bb83067
A3d3ffefe720fd771feb02374bb83067A3d3ffefe720fd771feb02374bb83067
A3d3ffefe720fd771feb02374bb83067Chris Waggoner
 
2nd Axiom Of Category Theory 1
2nd Axiom Of Category Theory 12nd Axiom Of Category Theory 1
2nd Axiom Of Category Theory 1Chris Waggoner
 
Things That Make You Go Hmmmm
Things That Make You Go HmmmmThings That Make You Go Hmmmm
Things That Make You Go HmmmmChris Waggoner
 
Irrationality in Economics
Irrationality in EconomicsIrrationality in Economics
Irrationality in EconomicsChris Waggoner
 

More from Chris Waggoner (6)

Visualizing Higher dimensions
Visualizing Higher dimensionsVisualizing Higher dimensions
Visualizing Higher dimensions
 
A3d3ffefe720fd771feb02374bb83067
A3d3ffefe720fd771feb02374bb83067A3d3ffefe720fd771feb02374bb83067
A3d3ffefe720fd771feb02374bb83067
 
2nd Axiom Of Category Theory 1
2nd Axiom Of Category Theory 12nd Axiom Of Category Theory 1
2nd Axiom Of Category Theory 1
 
Things That Make You Go Hmmmm
Things That Make You Go HmmmmThings That Make You Go Hmmmm
Things That Make You Go Hmmmm
 
Humility One Sheet
Humility One SheetHumility One Sheet
Humility One Sheet
 
Irrationality in Economics
Irrationality in EconomicsIrrationality in Economics
Irrationality in Economics
 

Recently uploaded

Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmaticsKotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmaticscarlostorres15106
 
Dev Dives: Streamline document processing with UiPath Studio Web
Dev Dives: Streamline document processing with UiPath Studio WebDev Dives: Streamline document processing with UiPath Studio Web
Dev Dives: Streamline document processing with UiPath Studio WebUiPathCommunity
 
DevEX - reference for building teams, processes, and platforms
DevEX - reference for building teams, processes, and platformsDevEX - reference for building teams, processes, and platforms
DevEX - reference for building teams, processes, and platformsSergiu Bodiu
 
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...shyamraj55
 
Ensuring Technical Readiness For Copilot in Microsoft 365
Ensuring Technical Readiness For Copilot in Microsoft 365Ensuring Technical Readiness For Copilot in Microsoft 365
Ensuring Technical Readiness For Copilot in Microsoft 3652toLead Limited
 
Advanced Test Driven-Development @ php[tek] 2024
Advanced Test Driven-Development @ php[tek] 2024Advanced Test Driven-Development @ php[tek] 2024
Advanced Test Driven-Development @ php[tek] 2024Scott Keck-Warren
 
Human Factors of XR: Using Human Factors to Design XR Systems
Human Factors of XR: Using Human Factors to Design XR SystemsHuman Factors of XR: Using Human Factors to Design XR Systems
Human Factors of XR: Using Human Factors to Design XR SystemsMark Billinghurst
 
APIForce Zurich 5 April Automation LPDG
APIForce Zurich 5 April  Automation LPDGAPIForce Zurich 5 April  Automation LPDG
APIForce Zurich 5 April Automation LPDGMarianaLemus7
 
WordPress Websites for Engineers: Elevate Your Brand
WordPress Websites for Engineers: Elevate Your BrandWordPress Websites for Engineers: Elevate Your Brand
WordPress Websites for Engineers: Elevate Your Brandgvaughan
 
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...Patryk Bandurski
 
Powerpoint exploring the locations used in television show Time Clash
Powerpoint exploring the locations used in television show Time ClashPowerpoint exploring the locations used in television show Time Clash
Powerpoint exploring the locations used in television show Time Clashcharlottematthew16
 
New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024BookNet Canada
 
Vertex AI Gemini Prompt Engineering Tips
Vertex AI Gemini Prompt Engineering TipsVertex AI Gemini Prompt Engineering Tips
Vertex AI Gemini Prompt Engineering TipsMiki Katsuragi
 
"Federated learning: out of reach no matter how close",Oleksandr Lapshyn
"Federated learning: out of reach no matter how close",Oleksandr Lapshyn"Federated learning: out of reach no matter how close",Oleksandr Lapshyn
"Federated learning: out of reach no matter how close",Oleksandr LapshynFwdays
 
My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024The Digital Insurer
 
Developer Data Modeling Mistakes: From Postgres to NoSQL
Developer Data Modeling Mistakes: From Postgres to NoSQLDeveloper Data Modeling Mistakes: From Postgres to NoSQL
Developer Data Modeling Mistakes: From Postgres to NoSQLScyllaDB
 
"LLMs for Python Engineers: Advanced Data Analysis and Semantic Kernel",Oleks...
"LLMs for Python Engineers: Advanced Data Analysis and Semantic Kernel",Oleks..."LLMs for Python Engineers: Advanced Data Analysis and Semantic Kernel",Oleks...
"LLMs for Python Engineers: Advanced Data Analysis and Semantic Kernel",Oleks...Fwdays
 
"Subclassing and Composition – A Pythonic Tour of Trade-Offs", Hynek Schlawack
"Subclassing and Composition – A Pythonic Tour of Trade-Offs", Hynek Schlawack"Subclassing and Composition – A Pythonic Tour of Trade-Offs", Hynek Schlawack
"Subclassing and Composition – A Pythonic Tour of Trade-Offs", Hynek SchlawackFwdays
 
Streamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupStreamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupFlorian Wilhelm
 

Recently uploaded (20)

Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmaticsKotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
 
Dev Dives: Streamline document processing with UiPath Studio Web
Dev Dives: Streamline document processing with UiPath Studio WebDev Dives: Streamline document processing with UiPath Studio Web
Dev Dives: Streamline document processing with UiPath Studio Web
 
DevEX - reference for building teams, processes, and platforms
DevEX - reference for building teams, processes, and platformsDevEX - reference for building teams, processes, and platforms
DevEX - reference for building teams, processes, and platforms
 
DMCC Future of Trade Web3 - Special Edition
DMCC Future of Trade Web3 - Special EditionDMCC Future of Trade Web3 - Special Edition
DMCC Future of Trade Web3 - Special Edition
 
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
 
Ensuring Technical Readiness For Copilot in Microsoft 365
Ensuring Technical Readiness For Copilot in Microsoft 365Ensuring Technical Readiness For Copilot in Microsoft 365
Ensuring Technical Readiness For Copilot in Microsoft 365
 
Advanced Test Driven-Development @ php[tek] 2024
Advanced Test Driven-Development @ php[tek] 2024Advanced Test Driven-Development @ php[tek] 2024
Advanced Test Driven-Development @ php[tek] 2024
 
Human Factors of XR: Using Human Factors to Design XR Systems
Human Factors of XR: Using Human Factors to Design XR SystemsHuman Factors of XR: Using Human Factors to Design XR Systems
Human Factors of XR: Using Human Factors to Design XR Systems
 
APIForce Zurich 5 April Automation LPDG
APIForce Zurich 5 April  Automation LPDGAPIForce Zurich 5 April  Automation LPDG
APIForce Zurich 5 April Automation LPDG
 
WordPress Websites for Engineers: Elevate Your Brand
WordPress Websites for Engineers: Elevate Your BrandWordPress Websites for Engineers: Elevate Your Brand
WordPress Websites for Engineers: Elevate Your Brand
 
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
 
Powerpoint exploring the locations used in television show Time Clash
Powerpoint exploring the locations used in television show Time ClashPowerpoint exploring the locations used in television show Time Clash
Powerpoint exploring the locations used in television show Time Clash
 
New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
 
Vertex AI Gemini Prompt Engineering Tips
Vertex AI Gemini Prompt Engineering TipsVertex AI Gemini Prompt Engineering Tips
Vertex AI Gemini Prompt Engineering Tips
 
"Federated learning: out of reach no matter how close",Oleksandr Lapshyn
"Federated learning: out of reach no matter how close",Oleksandr Lapshyn"Federated learning: out of reach no matter how close",Oleksandr Lapshyn
"Federated learning: out of reach no matter how close",Oleksandr Lapshyn
 
My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024
 
Developer Data Modeling Mistakes: From Postgres to NoSQL
Developer Data Modeling Mistakes: From Postgres to NoSQLDeveloper Data Modeling Mistakes: From Postgres to NoSQL
Developer Data Modeling Mistakes: From Postgres to NoSQL
 
"LLMs for Python Engineers: Advanced Data Analysis and Semantic Kernel",Oleks...
"LLMs for Python Engineers: Advanced Data Analysis and Semantic Kernel",Oleks..."LLMs for Python Engineers: Advanced Data Analysis and Semantic Kernel",Oleks...
"LLMs for Python Engineers: Advanced Data Analysis and Semantic Kernel",Oleks...
 
"Subclassing and Composition – A Pythonic Tour of Trade-Offs", Hynek Schlawack
"Subclassing and Composition – A Pythonic Tour of Trade-Offs", Hynek Schlawack"Subclassing and Composition – A Pythonic Tour of Trade-Offs", Hynek Schlawack
"Subclassing and Composition – A Pythonic Tour of Trade-Offs", Hynek Schlawack
 
Streamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupStreamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project Setup
 

surface area of a cylinder [∂ Campbell's soup can]