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### Course: Class 12 math (India)>Unit 5

Lesson 16: Derivatives capstone

# Common derivatives review

Review the differentiation rules for all the common function types.

## Polynomials

$\frac{d}{dx}\left(a{x}^{n}\right)=a\cdot n{x}^{n-1}$

$\frac{d}{dx}\sqrt[m]{\phantom{A}{x}^{n}}=\frac{d}{dx}\left({x}^{{}^{\frac{n}{m}}}\right)=\frac{n}{m}{x}^{{}^{\frac{n}{m}-1}}$

## Trigonometric functions

$\frac{d}{dx}\mathrm{sin}\left(x\right)=\mathrm{cos}\left(x\right)$
$\frac{d}{dx}\mathrm{cos}\left(x\right)=-\mathrm{sin}\left(x\right)$
$\frac{d}{dx}\mathrm{tan}\left(x\right)={\mathrm{sec}}^{2}\left(x\right)=\frac{1}{{\mathrm{cos}}^{2}\left(x\right)}$
$\frac{d}{dx}\mathrm{cot}\left(x\right)=-{\mathrm{csc}}^{2}\left(x\right)=-\frac{1}{{\mathrm{sin}}^{2}\left(x\right)}$
$\frac{d}{dx}\mathrm{sec}\left(x\right)=\mathrm{sec}\left(x\right)\mathrm{tan}\left(x\right)=\frac{\mathrm{sin}\left(x\right)}{{\mathrm{cos}}^{2}\left(x\right)}$
$\frac{d}{dx}\mathrm{csc}\left(x\right)=-\mathrm{csc}\left(x\right)\mathrm{cot}\left(x\right)=-\frac{\mathrm{cos}\left(x\right)}{{\mathrm{sin}}^{2}\left(x\right)}$

## Exponential functions

$\frac{d}{dx}\left({e}^{x}\right)={e}^{x}$
$\frac{d}{dx}\left({a}^{x}\right)=\mathrm{ln}\left(a\right)\cdot {a}^{x}$

## Logarithmic functions

$\frac{d}{dx}\mathrm{ln}\left(x\right)=\frac{1}{x}$
$\frac{d}{dx}{\mathrm{log}}_{b}\left(x\right)=\frac{1}{\mathrm{ln}\left(b\right)x}$

## Inverse trigonometric functions

$\frac{d}{dx}\mathrm{arcsin}\left(x\right)=\frac{1}{\sqrt{1-{x}^{2}}}$
$\frac{d}{dx}\mathrm{arccos}\left(x\right)=-\frac{1}{\sqrt{1-{x}^{2}}}$
$\frac{d}{dx}\mathrm{arctan}\left(x\right)=\frac{1}{1+{x}^{2}}$