The derivative of $si{n}^{-1}\left(\frac{2x}{1+x^2}\right)$ with respect to $ta{n}^{-1}\left(\frac{2x}{1-x^2}\right)$ is

Let $f\left(x\right)=lo{g}_e\left\{\frac{u\left(x\right)}{v\left(x\right)}\right\},u^{\prime }\left(2\right)=4,v^{\prime }\left(2\right)=2,u\left(2\right)=2,v\left(2\right)=1$, then $f^{\prime }\left(2\right)$ is equal to

If sin y = x sin (a + y) and $\frac{dy}{dx}=\frac{A}{1+x^2-2xcos{a}^{\prime }},$ then the value of A is

$If\sqrt{(x+y)}+\sqrt{(y-x)}=a,then\frac{d^{2}y}{d{x}^2}equals$

$Ifsin(x+y)=lo{g}_e(x+y),then\frac{dy}{dx}isequalto$

$If{x}^{cosy}+y^{cosx}=5.$ Then

$If\sqrt{(1-x^6)}+\sqrt{(1-y^6)}=a(x^3-y^3)and\frac{dy}{dx}=f(x,y)\sqrt{\left(\frac{1-y^6}{1-x^6}\right)},then$

If x = a $cos\theta ,y=bsin\theta ,then\frac{d^{3}y}{d{x}^3}$ is equal to

If $y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+....\infty ,}}}}$ then $\frac{dy}{dx}$ is equal to

The derivative of $co{s}^{-1}\left(\frac{x^{-1}-x}{x^{-1}+x}\right)atx=-1$ is