The chain rule provides a formula for finding the derivative of a composite function h(x) = f(g(x)). The formula is: h'(x) = f'(g(x))g'(x). This takes the derivative of the outer function f with respect to the inner function g, and multiplies it by the derivative of the inner function g. An example applies the chain rule to find the derivative of h(x) = (x3 + 4x)3/2 by identifying the inner and outer functions, taking their individual derivatives, and plugging into the chain rule formula.
Backpropagation: Understanding How to Update ANNs Weights Step-by-StepAhmed Gad
This presentation explains how the backpropagation algorithm is useful in updating the artificial neural networks (ANNs) weights using two examples step by step. Readers should have a basic understanding of how ANNs work, partial derivatives, and multivariate chain rule.
This presentation won`t dive directly into the details of the algorithm but will start by training a very simple network. This is because the backpropagation algorithm is meant to be applied over a network after training. So, we should train the network before applying it to catch the benefits of backpropagation algorithm and how to use it.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Backpropagation: Understanding How to Update ANNs Weights Step-by-StepAhmed Gad
This presentation explains how the backpropagation algorithm is useful in updating the artificial neural networks (ANNs) weights using two examples step by step. Readers should have a basic understanding of how ANNs work, partial derivatives, and multivariate chain rule.
This presentation won`t dive directly into the details of the algorithm but will start by training a very simple network. This is because the backpropagation algorithm is meant to be applied over a network after training. So, we should train the network before applying it to catch the benefits of backpropagation algorithm and how to use it.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Basic concepts of integration, definite and indefinite integrals,properties of definite integral, problem based on properties,method of integration, substitution, partial fraction, rational , irrational function integration, integration by parts, reduction formula, improper integral, convergent and divergent of integration
An Experiment to Determine and Compare Practical Efficiency of Insertion Sort...Tosin Amuda
Sorting is a fundamental operation in computer science (many programs use it as an intermediate step), and as a result a large number of good sorting algorithms have been developed. Which algorithm is best for a given application depends on—among other factors—the number of items to be sorted, the extent to which the items are already somewhat sorted, possible restrictions on the item values, and the kind of storage device to be used: main memory, disks, or tapes.
There are three reasons to study sorting algorithms. First, sorting algorithms illustrate many creative approaches to problem solving, and these approaches can be applied to solve other problems. Second, sorting algorithms are good for practicing fundamental programming techniques using selection statements, loops, methods, and arrays. Third, sorting algorithms are excellent examples to demonstrate algorithm performance.
However, this paper attempt to compare the practical efficiency of three sorting algorithms – Insertion, Quick and mere Sort using empirical analysis. The result of the experiment shows that insertion sort is a quadratic time sorting algorithm and that it’s more applicable to subarray that is sufficiently small. The merge sort performs better with larger size of input as compared to insertion sort. Quicksort runs the most efficiently.
Periodic Function, Dirichlet's Condition, Fourier series, Even & Odd functions, Euler's Formula for Fourier Coefficients, Change of Interval, Fourier series in the intervals (0,2l), (-l,l) , (-pi, pi), (0, 2pi), Half Range Cosine & Sine series Root mean square, Complex Form of Fourier series, Parseval's Identity
Basic concepts of integration, definite and indefinite integrals,properties of definite integral, problem based on properties,method of integration, substitution, partial fraction, rational , irrational function integration, integration by parts, reduction formula, improper integral, convergent and divergent of integration
An Experiment to Determine and Compare Practical Efficiency of Insertion Sort...Tosin Amuda
Sorting is a fundamental operation in computer science (many programs use it as an intermediate step), and as a result a large number of good sorting algorithms have been developed. Which algorithm is best for a given application depends on—among other factors—the number of items to be sorted, the extent to which the items are already somewhat sorted, possible restrictions on the item values, and the kind of storage device to be used: main memory, disks, or tapes.
There are three reasons to study sorting algorithms. First, sorting algorithms illustrate many creative approaches to problem solving, and these approaches can be applied to solve other problems. Second, sorting algorithms are good for practicing fundamental programming techniques using selection statements, loops, methods, and arrays. Third, sorting algorithms are excellent examples to demonstrate algorithm performance.
However, this paper attempt to compare the practical efficiency of three sorting algorithms – Insertion, Quick and mere Sort using empirical analysis. The result of the experiment shows that insertion sort is a quadratic time sorting algorithm and that it’s more applicable to subarray that is sufficiently small. The merge sort performs better with larger size of input as compared to insertion sort. Quicksort runs the most efficiently.
Periodic Function, Dirichlet's Condition, Fourier series, Even & Odd functions, Euler's Formula for Fourier Coefficients, Change of Interval, Fourier series in the intervals (0,2l), (-l,l) , (-pi, pi), (0, 2pi), Half Range Cosine & Sine series Root mean square, Complex Form of Fourier series, Parseval's Identity
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Embracing GenAI - A Strategic ImperativePeter Windle
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This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Module 6 the chain rule
1. THE CHAIN RULE
If 𝒇 and 𝒈 are differentiable functions, then the composite function 𝒉(𝒙) = 𝒇(𝒈(𝒙)) has derivative
given by:
𝒉′(𝒙) = 𝒇′(𝒈(𝒙))𝒈′(𝒙)
EXAMPLE 1: Differentiate 𝒉(𝒙) = (𝒙𝟑
+ 𝟒𝒙)
𝟑
𝟐
SOLUTION:
STEP 1 Identify the inner function and outer function
The inner function is: 𝒈(𝒙) = 𝒙𝟑
+ 𝟒𝒙
The outer function is: 𝒇(𝒙) = 𝒙
𝟑
𝟐
STEP 2 Solve for the derivative of the inner function and the outer function
• The inner function
𝒈(𝒙) = 𝒙𝟑
+ 𝟒𝒙
𝒈′(𝒙) = 𝟑𝒙𝟐
+ 𝟒
• The outer function
𝒇(𝒙) = 𝒙
𝟑
𝟐
𝒇′(𝒙) =
𝟑
𝟐
𝒙
𝟏
𝟐
STEP 3 Use the Chain Rule Formula
𝒉′(𝒙) = 𝒇′(𝒈(𝒙))𝒈′(𝒙)
𝒉′(𝒙) = (
𝟑
𝟐
𝒙
𝟏
𝟐)( 𝟑𝒙𝟐
+ 𝟒)
𝒉′(𝒙) = [
𝟑
𝟐
(𝒙𝟑
+ 𝟒𝒙)
𝟏
𝟐][𝟑𝒙𝟐
+ 𝟒]
![THE CHAIN RULE
If 𝒇 and 𝒈 are differentiable functions, then the composite function 𝒉(𝒙) = 𝒇(𝒈(𝒙)) has derivative
given by:
𝒉′(𝒙) = 𝒇′(𝒈(𝒙))𝒈′(𝒙)
EXAMPLE 1: Differentiate 𝒉(𝒙) = (𝒙𝟑
+ 𝟒𝒙)
𝟑
𝟐
SOLUTION:
STEP 1 Identify the inner function and outer function
The inner function is: 𝒈(𝒙) = 𝒙𝟑
+ 𝟒𝒙
The outer function is: 𝒇(𝒙) = 𝒙
𝟑
𝟐
STEP 2 Solve for the derivative of the inner function and the outer function
• The inner function
𝒈(𝒙) = 𝒙𝟑
+ 𝟒𝒙
𝒈′(𝒙) = 𝟑𝒙𝟐
+ 𝟒
• The outer function
𝒇(𝒙) = 𝒙
𝟑
𝟐
𝒇′(𝒙) =
𝟑
𝟐
𝒙
𝟏
𝟐
STEP 3 Use the Chain Rule Formula
𝒉′(𝒙) = 𝒇′(𝒈(𝒙))𝒈′(𝒙)
𝒉′(𝒙) = (
𝟑
𝟐
𝒙
𝟏
𝟐)( 𝟑𝒙𝟐
+ 𝟒)
𝒉′(𝒙) = [
𝟑
𝟐
(𝒙𝟑
+ 𝟒𝒙)
𝟏
𝟐][𝟑𝒙𝟐
+ 𝟒]](https://image.slidesharecdn.com/module6thechainrule-210225010723/85/Module-6-the-chain-rule-1-320.jpg)
