If $y = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \dots$,then $\frac{dy}{dx} = $

Find the derivative: $\frac{d}{dx} \sqrt{x \sin x}$

Differentiate the following with respect to $x$: $e^{\sin ^{-1} x}$

For the differentiable function $f: R - \{0\} \rightarrow R$,let $3 f(x) + 2 f\left(\frac{1}{x}\right) = \frac{1}{x} - 10$. Then $\left|f(3) + f^{\prime}\left(\frac{1}{4}\right)\right|$ is equal to

If $y=\left(\log _{\cot x} \tan x\right)\left(\log _{\tan x} \cot x\right)+\tan ^{-1}\left(\frac{4 x}{4-x^2}\right)$,then $\frac{d y}{d x}=$

Find the derivative of $f$ given by $f(x) = \tan^{-1} x$,assuming it exists.