# What is the derivative of y=4 sec ^2(x)?

Aug 15, 2014

$y ' = 8 {\sec}^{2} \left(x\right) \tan \left(x\right)$

Explanation :

let's start with general function, $y = {\left(f \left(x\right)\right)}^{2}$

differentiating with respect to $x$ Using Chain Rule,

$y ' = 2 \cdot f \left(x\right) \cdot f ' \left(x\right)$

Similarly following for given problem, yields

$y = 4 \cdot {\sec}^{2} \left(x\right)$

$y ' = 4 \cdot 2 \cdot \sec \left(x\right) \cdot \sec \left(x\right) \tan \left(x\right)$

$y ' = 8 {\sec}^{2} \left(x\right) \tan \left(x\right)$