Questions in differentiation

Select	Question
	If $y = {\tan ^{ - 1}}(\sec x - \tan x)$then $\frac{{dy}}{{dx}} = $
	If $y = {\cos ^{ - 1}}\cos (\|x\| - f(x)),$ where $$ $f(x)\left\{ \begin{array}{l} = 1\,,\,{\rm{if}}\,\,\,x > 0\\ = - 1\,,\,{\rm{if}}\,\,\,x < 0\\= 0\,,\,{\rm{if}}\,\,\,x = 0 \end{array} \right.$, then ${\left. {\frac{{dy}}{{dx}}} \right\|_{x = \frac{{5\pi }}{4}}}$ is
	If ${x^m}{y^n} = {(x + y)^{m + n}}$then ${\left. {\frac{{dy}}{{dx}}} \right\|_{x = 1,y = 2}}$ is equal to
	If $y = \frac{{{e^x} + {e^{ - x}}}}{{{e^x} - {e^{ - x}}}}$ then $\frac{{dy}}{{dx}}$ is equal to
	The derivative of function $f(x)$ is ${\tan ^4}x$. If $f(0) = 0$ then $\mathop {\lim }\limits_{x \to 0} \frac{{f(x)}}{x}$is equal to
	Let $f(x)$ be a polynomial function of the second degree. If $f(1) = f( - 1)$ and ${a_1},{a_2},{a_3}$ are in A.P. then $f'({a_1})$, $f'({a_2})$, $f'({a_3})$ are in
	If $r = {[2\varphi + {\cos ^2}(2\varphi + \pi /4)]^{1/2}}$ then what is the value of the derivative of $dr/d\varphi $ at $\varphi = \pi /4$
	If $f(x) = \cos x\cos 2x\cos 4x\cos 8x\cos 16x$, then $f'\left( {\frac{\pi }{4}} \right)$ is
	The derivative of $y = (1 - x)\,(2 - x)....(n - x)$ at $x = 1$ is equal to
	If $y = {\tan ^{ - 1}}\left( {\frac{{a\cos x - b\sin x}}{{b\cos x + a\sin x}}} \right)$ then $\frac{{dy}}{{dx}} = $