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

If $f(x) = (x - x_0)g(x)$,where $g(x)$ is continuous at $x_0$,then $f'(x_0)$ is equal to

Differentiate the function with respect to $x$: $\cos(x^{3}) \cdot \sin^{2}(x^{5})$

Find the derivative of the following function (it is to be understood that $a, b, c,$ and $d$ are fixed non-zero constants): $\frac{a x+b}{c x+d}$

Let $f: R \rightarrow R$ satisfy the equation $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$ and $f(x) \neq 0$ for any $x \in R$. If the function $f$ is differentiable at $x=0$ and $f'(0)=3$,then $\lim_{h \rightarrow 0} \frac{1}{h}(f(h)-1)$ is equal to ....... .

Derivative of $e^x$ with respect to $\sqrt{x}$ is