# Math Help - Differentiation

1. ## Differentiation

Find the derivative of $tan^{-1}(x^2)$.

Could someone explain how to solve this?

2. Originally Posted by Haris
Find the derivative of $tan^{-1}(x^2)$.

Could someone explain how to solve this?
Chain rule. Let $u = x^2$ so $y = \tan^{-1} u$. So

$\frac{dy}{dx} = \frac{dy}{du}\, \cdot \, \frac{du}{dx}$ and calculating each derivative gives $\frac{dy}{du} = \frac{1}{1+u^2}$ and $\frac{du}{dx} = 2x$.

Substituting gives

$\frac{dy}{dx} = \frac{1}{1+u^2}\, \cdot2x = \frac{2x}{1+x^4}.$