Basic Derivative Rules

Question	Answer
Derivatives	Derivatives
Basic Rules	Basic Rules
Constant Rule \[f(x)=k\]	\[f'(x)=0\]
Constant Multiple Rule \[f(x)=kx\]	\[f'(x)=k\]
Power Rule \[f(x)= x^\mathrm{n}\]	\[f'(x)= \mathrm{n}\cdot x^\mathrm{n-1}\]
Sum/Difference rule \[ y= f(x) + g(x) \]	\[ y'= f'(x) + g'(x) \]
Product Rule \[y = f(x)g(x) \]	\[y' = f(x)g'(x)+g(x)f'(x) \]
Quotient Rule \[y = \frac {f(x)} {g(x)} \]	\[y' = \frac {g(x)f'(x)-f(x)g'(x)} {\left( g(x) \right) ^2} \]
Trig derivatives	Trig derivatives
\[f(x)=\sin x\]	\[f'(x)=\cos x\]
\[f(x)=\cos x\]	\[f'(x)=-\sin x\]
\[f(x)=\tan x\]	\[f'(x)=\sec^2 x\]
\[f(x)=\sec x\]	\[f'(x)=\sec x \cdot \tan x\]
\[f(x)=\csc x\]	\[f'(x)= - \csc x \cdot \cot x\]
\[f(x)=\cot x\]	\[f'(x)= - \csc^2 x \]
\[f(x)=\tan^{-1} x\]	\[f'(x)= \frac{1}{1+x^2} \]
\begin{equation} \frac{d}{dx} \left[ \sin^{-1}x \right] = \end{equation}	\begin{equation} \frac{1}{\sqrt{1-x^2}} \end{equation}

Resource summary

	Created by Bill Andersen over 9 years ago

	Copied by Brandon Anderson about 5 years ago