Calculus
Intermediate

Chain Rule

Derivative of a composite function.

Formula

dydx=dydududx\frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}

Variables

y,uFunctions

Example

d/dx sin(x²)=2x cos(x²)

Did You Know?

The chain rule is what makes modern neural networks trainable, powering the backpropagation algorithm.

derivative