For some constants $a$ and $b$,find the derivative of $(x-a)(x-b)$.

Which one of the following is false?

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

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

The differential coefficient of $f(\sin x)$ with respect to $x,$ where $f(x) = \log x,$ is

The values of $x$,at which the first derivative of the function $(\sqrt{x} + \frac{1}{\sqrt{x}})^2$ with respect to $x$ is $\frac{3}{4}$,are