Questions in differentiation

Select	Question
	If $y = \frac{{{a^{{{\cos }^{ - 1}}x}}}}{{1 + {a^{{{\cos }^{ - 1}}x}}}}$and $z = {a^{{{\cos }^{ - 1}}x}}$, then $\frac{{dy}}{{dx}}$=
	If $f(x) = (x - {x_0})g(x)$, where $g(x)$ is continuous at ${x_0}$, then $f'({x_0})$ is equal to
	If$y = {\log _{\sin x}}(\tan x),$ then ${\left( {\frac{{dy}}{{dx}}} \right)_{\pi /4}} = $
	If $y = {\log _2}[{\log _2}(x)]$, then $\frac{{dy}}{{dx}}$is equal to
	$\frac{d}{{dx}}({e^{{x^3}}})$ is equal to
	$\frac{d}{{dx}}({\sin ^{ - 1}}x)$ is equal to
	If $y = {\tan ^{ - 1}}\sqrt {\frac{{1 + \cos x}}{{1 - \cos x}}} $, then $\frac{{dy}}{{dx}}$ is equal to
	If $y = \frac{{{{\sin }^{ - 1}}x}}{{\sqrt {1 - {x^2}} }}$, then $(1 - {x^2})\frac{{dy}}{{dx}}$ is equal to
	Differential coefficient of ${\sec ^{ - 1}}x$ is
	If $f(2) = 4$, $f'(2) = 1$then $\mathop {\lim }\limits_{x \to 2} \frac{{xf(2) - 2f(x)}}{{x - 2}} = $