Derivative of $e^x$ with respect to $\sqrt{x}$ is

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

Compute the derivative of $f(x) = \sin 2x$.

$\frac{d}{dx} \log(\log x) =$

Let $f(x) = \sum_{k=1}^{10} kx^k$,$x \in R$. If $2f(2) + f'(2) = 119(2)^n + 1$,then $n$ is equal to $..........$.

Find $\frac{dy}{dx}$ if $x-y=\pi$.