If $f(x) = mx + c$,$f(0) = 1$,and $f'(0) = 1$,then find the value of $f(2)$.

If $f: R \rightarrow R$ is an even function having derivatives of all orders, then which of the following is an odd function?

If $f(x) = \sum_{p=1}^7 p^2 \sin^{-1}\left(\frac{4}{5} \sin(px) - \frac{3}{5} \cos(px)\right)$, then the value of $\frac{df}{dx}$ at $x = 1$ is (Given that $\sin^{-1}(\sin x) = x$)

Differentiate the function with respect to $x$: $2 \sqrt{\cot \left(x^{2}\right)}$

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

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): $(ax^{2} + \sin x)(p + q \cos x)$