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

Find the derivative of the function $\sin x$ at the point $x=\frac{\pi }{2}$.

Find the derivative of the function $x$ at the point $x=1$.

Find the derivative of the function $2\cos x$ at the point $x=\frac{\pi }{2}$.

Find the derivative of the function $\sin 2x$ at the point $x=\frac{\pi }{2}$.

Differentiate $\frac{2}{x}$ using first principle.

Differentiate $\frac{1}{\sqrt{x}}$ using first principle.

Differentiate $\frac{1}{x^3}$ using first principle.

Differentiate $\frac{x^2+1}{x}$ using first principle.