If $f(x) = \sqrt{ax} + \frac{a^2}{\sqrt{ax}}$, then $f^{\prime}(a)$ is equal to

Let $f(x) = x - 5$. If $g(x) = [f(4h(x) + 3)]^2$ and $h(1) = 4, h'(1) = -2$, then $g'(1) = .....$

$\frac{d}{dx}(\sin^{-1}x)$ is equal to

Let for a differentiable function $f:(0, \infty) \rightarrow \mathbb{R}$,$f(x)-f(y) \geq \log_e\left(\frac{x}{y}\right)+x-y, \forall x, y \in(0, \infty)$. Then $\sum_{n=1}^{20} f^{\prime}\left(\frac{1}{n^2}\right)$ is equal to

If $h(x) = \sqrt{4f(x) + 3g(x)}$,$f(1) = 4$,$g(1) = 3$,$f'(1) = 4$,and $g'(1) = 3$,then find $h'(1)$.

If $y = \log {\left( \frac{1 + x}{1 - x} \right)^{1/4}} - \frac{1}{2}{\tan ^{ - 1}}x,$ then $\frac{dy}{dx} = $