Derivatives of Composite Functions formulas

The chain rule - general formula for composite functions

$\left(f\left(g(x)\right)\right)'=f'(g(x))\cdot g'(x)$

$\left(f^2\right)'=2\cdot f \cdot f'$

$\left(f^n\right)'=n \cdot f^{n-1} \cdot f'$

$\left(\sqrt{f}\right)' = \dfrac{f'}{2\sqrt{f}}$

$\left( \sin f\right)'=\cos f \cdot f'$

$\left( \cos f \right)' = - \sin f \cdot f'$

$\left( \tan f \right)' = \dfrac{f'}{\cos f^2}$

$\left( e^f \right)' = e^f \cdot f'$

$\left( \ln f \right)' = \dfrac{f'}{f}$

10.

$\left( \log_a x \right)'=\dfrac{f'}{f \ln a}$

11.

$\left( a^x\right)' = a^f \cdot \ln a \cdot f'$