If $f(x) = \frac{g(x) + g(-x)}{2} + \frac{2}{[h(x) + h(-x)]^{-1}}$,where $g$ and $h$ are differentiable functions,then find $f^{\prime}(0)$.

If $f(2) = 4$ and $f'(2) = 1$,then $\mathop {\lim }\limits_{x \to 2} \frac{xf(2) - 2f(x)}{x - 2} = $

Find the derivative of the following function: $2 \tan x - 7 \sec x$.

People living on Mars,instead of the usual definition of derivative $D f(x)$,define a new kind of derivative,$D^*f(x)$ by the formula $D^*f(x) = \lim_{h \to 0} \frac{f^2(x + h) - f^2(x)}{h}$ where $f^2(x)$ means $[f(x)]^2$. If $f(x) = x \ln x$,then the value of $\left. D^*f(x) \right|_{x = e}$ is:

$\frac{d}{dx} [\operatorname{cosech}^{-1}(\tan 2x)] = $

If $f(x^{5}) = 5x^{3}$,then $f'(x)$ is equal to