If $f(x) = x \tan^{-1} x$,then $\lim_{x \rightarrow 1} \frac{f(x) - f(1)}{x - 1}$ is equal to

If $f(x) = \sin \left(\cosh \left(\frac{x^2+1}{x^2+2}\right)\right)$, then $f^{\prime}(1) = $

Find the derivative of $\frac{x^{n}-a^{n}}{x-a}$ with respect to $x$,where $a$ is a constant.

$\frac{d}{dt}(\tan t + t^2 \operatorname{cosech} t)$ is equal to

Let $3f(x) - 2f(1/x) = x,$ then $f'(2)$ is equal to

If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{x-2}{x^2-3x+2} & \text{if } x \in R - \{1, 2\} \\ 2 & \text{if } x = 1 \\ 1 & \text{if } x = 2 \end{cases}$,then find $\lim_{x \rightarrow 2} \frac{f(x)-f(2)}{x-2}$.