Find the derivative of $(5x^{3} + 3x - 1)(x - 1)$.

Find the derivative of $f$ given by $f(x) = \sin^{-1} x$ assuming it exists.

If $y = \sqrt{\sin \sqrt{x}}$,then $\frac{dy}{dx} = $

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 ....... .

If $y=\sqrt{2 x+\cos ^2\left(2 x+\frac{\pi}{4}\right)}$,then find $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$.

If $3 f(x)-2 f\left(\frac{1}{x}\right)=x$,then $f^{\prime}(2)$ is equal to