Compute the derivative of $f(x) = \sin^{2} x$.

If $y = \log \tan \sqrt{x}$,then the value of $\frac{dy}{dx}$ is

If $y = \sinh^{-1}\left(\frac{1-x}{1+x}\right)$,then find $\frac{dy}{dx}$.

Let $f(x)$ be a continuous and differentiable function for all real numbers. If $f(x + y) = f(x) - 3xy + f(y)$ and $\lim_{h \to 0} \frac{f(h)}{h} = 7$,then the value of $f'(x)$ is:

$\frac{d}{dx}\left[ \frac{2}{\pi }\sin {x^\circ} \right] = $

$\frac{d}{d x}\left[a \tan ^{-1} x+b \log \left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^4-1}$
$\Rightarrow a-2 b$ is equal to