If $f(x) = x + 2,$ then $f'(f(x))$ at $x = 4$ is

If $y = \tan^{-1} \left[ \frac{4 \sin 2x}{\cos 2x - 6 \sin^2 x} \right]$,then $\frac{dy}{dx}$ at $x = 0$ is

Differentiate the function with respect to $x$: $\sin (ax+b)$

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

Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f''(x) = g''(x)$ for all $x \in R$, $f'(1) = 2g'(1) = 4$ and $g(2) = 3f(2) = 9$. Then $f(25) - g(25)$ is equal to:

If $f(x) = \sqrt{1 + \cos^2(x^2)}$,then $f'\left(\frac{\sqrt{\pi}}{2}\right)$ is