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

Find the derivative of the following function: $\frac{x}{\sin^{n} x}$ (where $n$ is an integer).

The differential coefficient of ${\left( {{x^{\frac{{\ell + m}}{{m - n}}}}} \right)^{\frac{1}{{n - \ell }}}} \cdot {\left( {{x^{\frac{{m + n}}{{n - \ell }}}}} \right)^{\frac{1}{{\ell - m}}}} \cdot {\left( {{x^{\frac{{n + \ell }}{{\ell - m}}}}} \right)^{\frac{1}{{m - n}}}}$ with respect to $x$ is:

If $y=\log \left[\tan \sqrt{\frac{2^x-1}{2^x+1}}\right], x>0$, then $\left(\frac{d y}{d x}\right)_{x=1}=$

If $y = \frac{\sin^{-1} x}{\sqrt{1 - x^2}}$,then $(1 - x^2)\frac{dy}{dx}$ is equal to

If $y = b \cos \log \left( \frac{x}{n} \right)^n$,then $\frac{dy}{dx} = $