3127600
Description
Flashcards by Bill Andersen, updated more than 1 year ago
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Created by Bill Andersen
over 9 years ago
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| 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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