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

Find the derivative: $\frac{d}{dx} \tan^{-1} \left( \frac{ax - b}{bx + a} \right) = $

If $y = \sin [\cos (\sin x)],$ then $dy/dx = $

Suppose $f(x)$ is differentiable at $x = 1$ and $\mathop {\lim }\limits_{h \to 0} \frac{1}{h}f(1 + h) = 5$,then $f'(1)$ equals

If $y = \frac{(1 - x)^2}{x^2}$,then $\frac{dy}{dx}$ is

If $f(x) = \sum_{p=1}^7 p^2 \sin^{-1}\left(\frac{4}{5} \sin(px) - \frac{3}{5} \cos(px)\right)$, then the value of $\frac{df}{dx}$ at $x = 1$ is (Given that $\sin^{-1}(\sin x) = x$)