\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}

Chain rule is used to decompose working with complex equations within differentiation much easier.

It allows you to substitute in a variable for a complex part of the equation, working with it in a much simpler manner.

Example

y = 4 (2 x^{3} + 7)^{4} y = 4 u^{4} u = 2 x^{3} + 7 \frac{d y}{d u} = 16 u^{3} \frac{d u}{d x} = 6 x^{2} \frac{d y}{d u} \times \frac{d u}{d x} = 16 u^{3} \times 6 x^{2} \frac{d y}{d x} = 16 (2 x^{+} 7) \times 6 x^{2}

Chain Rule