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Make Your Own Neural Network in Python

Chain Rule

Explore the chain rule in calculus to understand how derivatives of composite functions can be calculated step-by-step. This lesson helps you grasp the method to simplify complex derivative problems into manageable parts, essential for optimizing neural networks.

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Derivative of a function of a function

Imagine a function

f=y2f=y^2

where yy is itself:

y=x3+xy=x^3+x

We can write this as f=(x3+x)2f = (x^3 + x)^2 if we want to.

How does ff change with yy? That is, what is ∂f/∂y\partial f / \partial y? This is easy as we just apply the power rule we just developed, multiplying and reducing the power, so ∂f/∂y=2y\partial f / \partial y= 2y.

How does ff change with xx? Well, we ...