Basic Derivative Rules

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Basic Derivative Rules
Bill Andersen
Flashcards by Bill Andersen, updated more than 1 year ago
Bill Andersen
Created by Bill Andersen over 8 years ago
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Resource summary

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
\[f(x)=\sin x\] \[f'(x)=\cos x\]
\[f(x)=\cos x\] \[f'(x)=-\sin x\]
\[f(x)=\tan x\] \[f'(x)=\sec^2 x\]
\[f(x)=\sec x\] \[f'(x)=\sec x \cdot \tan x\]
\[f(x)=\csc x\] \[f'(x)= - \csc x \cdot \cot x\]
\[f(x)=\cot x\] \[f'(x)= - \csc^2 x \]
\[ f(x)= \sin^{-1}x \] \[ f'(x)=\frac{1}{\sqrt{1-x^2}} \]
\[f(x)= \cos^{-1}x \] \[ f'(x)=\frac{-1}{\sqrt{1-x^2}}\]
\[f(x)=tan^{-1}x\] \[f'(x)=\frac{1}{1+x^2}\]
\[f(x)=cot^{-1}x\] \[f'(x)=\frac{-1}{1+x^2}\]
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