Questions in differentiation

Select	Question
	Differential coefficient of ${{\tan }^{-1}}\sqrt{\frac{1-{{x}^{2}}}{1+{{x}^{2}}}}$ w.r.t. ${{\cos }^{-1}}({{x}^{2}})$ is
	If $u={{\tan }^{-1}}\left\{ \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right\}$ and $v=2{{\tan }^{-1}}x$, then $\frac{du}{dv}$ is equal to
	The derivative of ${{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\,$w.r.t. ${{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)$ is
	The derivative of ${{\sin }^{2}}x$with respect to ${{\cos }^{2}}x$ is
	Differential coefficient of ${{\tan }^{-1}}\left( \frac{x}{1+\sqrt{1-{{x}^{2}}}} \right)$ w.r.t ${{\sin }^{-1}}x,$ is
	The derivative of ${{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)$ w.r.t. ${{\cot }^{-1}}\left( \frac{1-3{{x}^{2}}}{3x-{{x}^{2}}} \right)$ is
	The differential of ${{e}^{{{x}^{3}}}}$with respect to $\log x$ is
	The 2nd derivative of $a{{\sin }^{3}}t$ with respect to $a{{\cos }^{3}}t\,\,\text{at}\,\,t=\frac{\pi }{4}$ is
	The differential coefficient of $f(\sin x)$ with respect to x, where $f(x)=\log x$, is
	If $y=\sin x\sin 3x,$then ${{y}_{n}}=$