$\frac{d}{dx}(e^{x\sin x}) = $

For some constants $a$ and $b$,find the derivative of $\frac{x-a}{x-b}$.

Let $f$ be a differentiable function such that $f(1) = 2$ and $f'(x) = f(x)$ for all $x \in R$. If $h(x) = f(f(x))$,then $h'(1)$ is equal to

Find the derivative of the following function (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers): $(ax + b)^n (cx + d)^m$

If $y=\frac{\cos x}{1+\sin x}$,then
$(a)$ $\frac{dy}{dx}=\frac{-1}{1+\sin x}$
$(b)$ $\frac{dy}{dx}=\frac{1}{1+\sin x}$
$(c)$ $\frac{dy}{dx}=-\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{x}{2}\right)$
$(d)$ $\frac{dy}{dx}=\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{x}{2}\right)$

If $f(x) = \frac{1}{1 + \frac{1}{x}}$ and $g(x) = \frac{1}{1 + \frac{1}{f(x)}}$, then $g^{\prime}(2)$ is equal to