Question

Differentiate $\sec x^{\tan x}$ with respect to $x$

Answer 1

$\frac{d}{dx}\left[\sec x^{\tan x}\right]$

$=\sec x^{\tan x}.\frac{d}{dx}\left[lu\left(\sec x\tan x\right)\right]$

$={\sec }^{\tan x}x\left({\sec }^{2}xlu\left(\sec x\right)+\frac{\sec x{\tan }^{2}x}{\sec x}\right)$

$={\sec }^{\tan x}x\left({\sec }^{2}xlu\left(\sec x\right)+{\tan }^{2}x\right)$