Questions in differentiation

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	Let $g(x)$ be the inverse of the function $f(x)$ and $f'(x) = \frac{1}{{1 + {x^3}}}$. Then $g'(x)$ is equal to
	Let f and g be differentiable functions satisfying $g'(a) = 2,$ $g(a) = b$ and $fog = I$(identity function). Then $f'(b)$ is equal to
	The differential coefficient of $f[\log (x)]$ when $f(x) = \log x$ is
	The derivative of $F[f\{ \varphi (x)\} ]$ is
	Let $f(x) = {e^x}$, $g(x) = {\sin ^{ - 1}}x$ and $h(x) = f(g(x)),$ then $h'(x)/h(x) = $
	If ${x^2} + {y^2} = t - \frac{1}{t},$${x^4} + {y^4} = {t^2} + \frac{1}{{{t^2}}}$, then ${x^3}y\frac{{dy}}{{dx}} = $
	If $x = a\sin 2\theta (1 + \cos 2\theta ),y = b\cos 2\theta (1 - \cos 2\theta )$, then $\frac{{dy}}{{dx}} = $
	If $\sin y = x\cos (a + y),$ then $\frac{{dy}}{{dx}} = $
	If $x = \frac{{3at}}{{1 + {t^3}}},y = \frac{{3a{t^2}}}{{1 + {t^3}}},$then $\frac{{dy}}{{dx}}$=
	If $x = t + \frac{1}{t},y = t - \frac{1}{t},$then $\frac{{{d^2}y}}{{d{x^2}}}$is equal to