If $f(x) = \cos x \cos 2x \cos 4x \cos 8x \cos 16x$, then $f'\left(\dfrac{\pi}{4}\right)$ is equal to

Let f(x) be a twice differentiable function such that $f''(x) = -f(x)$, $f'(x) = g(x)$ and $h(x) = \{f(x)\}^2 + \{g(x)\}^2$. If $h(5) = 11$, then $h(10)$ is equal to ...

If $\cot[f(x)] = \dfrac{3x - x^3}{1 - 3x^2}$ and $\sin[g(x)] = \dfrac{1 - x^2}{1 + x^2}$, then $\lim\limits_{x \to t}\dfrac{f(x) - f(t)}{g(x) - g(t)} = \ldots$

If $y = \cos^{-1}\left(\dfrac{1 - 4^x}{1 + 4^x}\right)$, then $\dfrac{dy}{dx}$ at $x = 1$ is