If $y = \cos(\sin x^2)$,then $\frac{dy}{dx}$ at $x = \sqrt{\frac{\pi}{2}}$ is

If $y = \frac{(a - x)\sqrt{a - x} - (b - x)\sqrt{x - b}}{\sqrt{a - x} + \sqrt{x - b}}$,then $\frac{dy}{dx}$ wherever it is defined is equal to:

Let $f: \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow \mathbb{R}$ be a differentiable function such that $f(0)=\frac{1}{2}$. If $\lim _{x \rightarrow 0} \frac{x \int_0^x f(t) dt}{e^{x^2}-1}=\alpha$,then $8 \alpha^2$ is equal to:

Differentiate the following with respect to $x$: $e^{\sin ^{-1} x}$

$\frac{d}{dx}({x^2} + \cos x)^4 = $

If $y = f \left( \frac{2x - 1}{x^2 + 1} \right)$ and $f'(x) = \sin x$,then $\frac{dy}{dx} = $