Questions in differentiation

Select	Question
	If $\sin y = x\sin (a + y),$then $\frac{{dy}}{{dx}} = $
	If $\tan (x + y) + \tan (x - y) = 1,$then $\frac{{dy}}{{dx}} = $
	If $y\sec x + \tan x + {x^2}y = 0$, then $\frac{{dy}}{{dx}}$=
	If $\sin (xy) + \frac{x}{y} = {x^2} - y,$then $\frac{{dy}}{{dx}} = $
	If ${\sin ^2}x + 2\cos y + xy = 0$, then $\frac{{dy}}{{dx}} = $
	If ${x^3} + 8xy + {y^3} = 64$,then $\frac{{dy}}{{dx}} = $
	If $a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$, then $\frac{{dy}}{{dx}} = $
	If $y = f\left( {\frac{{5x + 1}}{{10{x^2} - 3}}} \right)$and $f'(x) = \cos x$, then $\frac{{dy}}{{dx}} = $
	If$f(x) = \frac{1}{{1 - x}}$, then the derivative of the composite function $f[f\{ f(x)\} ]$ is equal to
	Let g (x) be the inverse of an invertible function $f(x)$ which is differentiable at x = c, then $g'(f(c))$ equals