If $f$ is differentiable, $f(x+y)=f(x) f(y)$ for all $x, y \in R$, $f(3)=3$, and $f^{\prime}(0)=11$, then $f^{\prime}(3)$ is equal to:

Let $f(x + y) = f(x) + f(y)$ and $f(x) = x^2 g(x)$ for all $x, y \in R$,where $g(x)$ is a continuous function. Then $f'(x)$ 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): $\frac{ax+b}{px^{2}+qx+r}$

Find the derivative of the following function (it is to be understood that $a, b, c$ are fixed non-zero constants): $\frac{1}{ax^{2}+bx+c}$

Find the derivative of the following function (it is to be understood that $p, q, r$ are fixed non-zero constants): $\frac{p x^{2}+q x+r}{x}$

If $f(x) = \sqrt{1 + \cos^2(x^2)}$,then $f^{\prime}\left(\frac{\sqrt{\pi}}{2}\right)$ is