Stage 2 · Lesson 4 of 9
The chain rule
gives the derivative of a function inside another function. If y = f(g(x)), then dy/dx = f'(g(x)) × g'(x): you multiply the rates of change along the chain. For y = (3x + 1)², the outer part gives 2(3x + 1) and the inner part gives 3, so dy/dx = 6(3x + 1).
A neural network is a long chain of functions like this. , the way networks learn, is the chain rule applied from the loss back through every , reusing each result it has already worked out. This makes easy to picture: multiply many numbers smaller than 1 and the product shrinks towards zero.
Common trapmemorising the formula without being able to trace it through a small , a diagram of each step in a calculation.
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Resources for this stage
Start with· follow one of these
- CoursePaidMathematics for Machine Learning and Data Science Specialization
DeepLearning.AI · Beginner · Coursera subscription; financial aid available
Paid, with financial aid: linear algebra, calculus and statistics taught visually with Python labs
- CourseFreeKhan Academy Statistics and Probability
Khan Academy · Beginner
Free, complete statistics and probability with practice questions on every topic
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Also worth your time
- Mathematics for Machine LearningGo deeper
Free book that ties the maths directly to regression, PCA and classifiers