# What is the derivative of y=sec^2(x)?

Sep 21, 2014

We need to use the chain rule

$y = {\sec}^{2} \left(x\right)$

Let $u = \sec \left(x\right)$

$u ' = \sec \left(x\right) \tan \left(x\right)$

$y = {u}^{2}$

$y ' = 2 u \cdot u '$

$y ' = 2 \sec \left(x\right) \cdot \sec \left(x\right) \tan \left(x\right) = 2 {\sec}^{2} \left(x\right) \tan \left(x\right)$