Question

Find $\frac{dy}{dx}$ for $y=\frac{\tan x}{x}\log x^x$.

Answer 1

Now,

$y=\frac{\tan x}{x}\log x^x$

or, $y=\frac{\tan x}{x}\left(x\log x\right)$

or, $y=\tan x.\log x$.

Now differentiating both sides with respect to $x$ we get,

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