# Chain Rule Formula

The Chain Rule is a formula for computing the derivative of the composition of two or more functions. For instance, if f and g are functions, then the chain rule expresses the derivative of their composition.

The Chain Rule Formula is as follows –

$\LARGE \frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}$

### Solved Examples

Question 1: Differentiate y = cos $x^{2}$

Solution:

Given,

y = cos $x^{2}$

Let u = $x^{2}$, so that y = cos u

Therefore: $\frac{du}{dx}$=2x

$\frac{du}{dx}$ = -sin u

And so, the chain rule says:

$\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}$

$\frac{dy}{dx}$= -sin u $\times$ 2x

= -2x sin u $x^{2}$