Let $f(x)$ and $g(x)$ be differentiable functions on $R$. If $h(x) = f(g(f(x)))$,where $f(2) = 1$,$g(1) = 2$ and $f'(2) = g'(1) = 4$,then $h'(2)$ is equal to:

If $y = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \dots$,then $\frac{dy}{dx} = $

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

$\mathop {\text{Limit}}\limits_{h \to 0} \frac{{\int\limits_a^{x + h} {\ln^2 t \, dt} - \int\limits_a^x {\ln^2 t \, dt} }}{h} = $

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 $\lim_{x \rightarrow 2} \frac{f(x)-f(2)}{x-2}$.

The value of $\frac{d}{{d(\ln x)}}({e^x}{\ln ^2}x)$ at $x=e$ is: