If $$y^2=a x^2+b x+c$$, where $$a, b, c$$ are constants, then $$y^3 \frac{d^2 y}{d x^2}$$ is equal to

$$x=\frac{1-t^2}{1+t^2}$$ and $$y=\frac{2 a t}{1+t^2}$$, then $$\frac{d y}{d x}=$$

If y = 2 sin x + 3 cos x and y + A$$\mathrm{\frac{d^2y}{dx^2}}$$ = B, then the values of A, B are respectively

If $$y = {\tan ^{ - 1}}\left\{ {{{a\cos x - b\sin x} \over {b\cos x + a\sin x}}} \right\}$$, then $${{dy} \over {dx}}$$