First Principle of Differentiation

On differentiating  $\sqrt{\tan x}$ with respect to $x$ from first principle, the solution would be:

Derivative of $\sin x$

Find the derivative of $f\left(x\right)=\left(x-1\right)\left(x-2\right)$ by using first principle. 

What is the derivative of $\sin x?$

If $f\left(x\right)=\left[\begin{array}{ll}x{\tan }^{-1}x+{\sec }^{-1}\left(\frac{1}{x}\right),& x\in \left(-1,1\right)-\left\{0\right\}\\ \frac{\pi }{2}& \mathrm{if} x=0\end{array}\right.$, then $f^{\text{'}}\left(0\right)$ is

Compute the derivative of $\tan x$.

Compute the derivative of $\sin x$.

Find the derivative of $f\left(x\right)=1+x+x^2+x^3+\dots +x^{50}$ at $x=1$.

Compute the derivative of $6x^{100}-x^{55}+x$.

Find the derivative of $f\left(x\right)=\frac{1}{x}$.

Find the derivative of the constant function $f\left(x\right)=a$ for a fixed real number $a$.

Find the derivative of $f\left(x\right)=x^2$.

Find the derivative of $f\left(x\right)=10x$.

Find the derivative of $f\left(x\right)=3$ at $x=0$ and at $x=3$.

Find the derivative of $\sin x$ at $x=0$.

Find the derivative of the function $f\left(x\right)=2x^2+3x-5$ at $x=-1$. Also prove that $f\text{'}\left(0\right)+3f\text{'}\left(-1\right)=0$.

Find the derivative at $x=2$ of the function $f\left(x\right)=3x$.

If $Y=x\left(x-1\right)\left(x-2\right)$ then $dy/dx$ is

Find the velocity of a particle moving on a line at $t=3 sec$, if its position is in meters when 

(i) $s=\sin \left(\frac{ t}{9}\right)$