If $f'(x)$ is zero in the interval $(a, b)$,then in this interval it is

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:

Differentiate $a^{x}$ with respect to $x$,where $a$ is a positive constant.

Differentiate the following with respect to $x$: $\sin \left(\tan ^{-1} e^{-x}\right)$

Find the derivative of the function: $\frac{x}{1+\tan x}$

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