Find the derivative of $x^{-4}(3-4x^{-5})$.

If $f(t) = \frac{t}{2} + \frac{1}{4} \log(2t - 1)$,then $f^{\prime}\left(\frac{t+1}{2t+1}\right) = $

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 ....... .

$\frac{d}{dx}(\sin^{-1}x)$ is equal to

If $f(x)=\operatorname{cosec}^{-1}\left[\frac{10}{6 \sin \left(2^x\right)-8 \cos \left(2^x\right)}\right]$,then $f^{\prime}(x)$ is equal to:

Differentiate the function with respect to $x$: $\cos (\sqrt{x})$