If the function $f(x)$ is defined by $f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + \dots + \frac{x^2}{2} + x + 1$,then $f'(0) = $

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:

The differential coefficient of $\sqrt{\sec \sqrt{x}}$ is

$\frac{d}{dx}[e^{ax} \cos(bx + c)] = ?$

If $T = 2 \pi \sqrt{\frac{L}{g}}$,where $g$ is a constant and the relative error in $T$ is $k$ times the percentage error in $L$,then $\frac{1}{k} =$

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 $\sin^{-1}(\sin x) = x$)