Basic Derivative Rules

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