Question

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

Answer 1

$y=x^{\tan x}$

By taking log in Both Sides

$\log y=\tan x\log x$

$\frac{1}{y}\frac{dy}{dx}=\frac{\tan x}{x}+{\sec }^{2}x\log x$

$\frac{dy}{dx}=x^{\tan x}[\frac{\tan x}{x}+{\sec }^{2}x\log x]$