Flashcards
Basic Derivative Rules
Cards in this deck (19)
- 1DerivativesDerivatives
- 2Basic RulesBasic Rules
- 3Constant Rule \[f(x)=k\]\[f'(x)=0\]
- 4Constant Multiple Rule \[f(x)=kx\]\[f'(x)=k\]
- 5Power Rule \[f(x)= x^\mathrm{n}\]\[f'(x)= \mathrm{n}\cdot x^\mathrm{n-1}\]
- 6Sum/Difference rule \[ y= f(x) + g(x) \]\[ y'= f'(x) + g'(x) \]
- 7Product Rule \[y = f(x)g(x) \]\[y' = f(x)g'(x)+g(x)f'(x) \]
- 8Quotient Rule \[y = \frac {f(x)} {g(x)} \]\[y' = \frac {g(x)f'(x)-f(x)g'(x)} {\left( g(x) \right) ^2} \]
- 9Trig derivativesTrig derivatives
- 10\[f(x)=\sin x\]\[f'(x)=\cos x\]
- 11\[f(x)=\cos x\]\[f'(x)=-\sin x\]
- 12\[f(x)=\tan x\]\[f'(x)=\sec^2 x\]
- 13\[f(x)=\sec x\]\[f'(x)=\sec x \cdot \tan x\]
- 14\[f(x)=\csc x\]\[f'(x)= - \csc x \cdot \cot x\]
- 15\[f(x)=\cot x\]\[f'(x)= - \csc^2 x \]
- 16\[ f(x)= \sin^{-1}x \]\[ f'(x)=\frac{1}{\sqrt{1-x^2}} \]
- 17\[f(x)= \cos^{-1}x \]\[ f'(x)=\frac{-1}{\sqrt{1-x^2}}\]
- 18\[f(x)=tan^{-1}x\]\[f'(x)=\frac{1}{1+x^2}\]
- 19\[f(x)=cot^{-1}x\]\[f'(x)=\frac{-1}{1+x^2}\]