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the LIMIT definition of a derivative

f'(x)=\frac{\lim}{h>0} [\frac{f(x+h)-f(x)}{h}]

The Power Rule

\frac{d}{dx} x^{n} = n\times x^{n-1}

The Sum and Difference Rule

(f\pm g)'=f'\pm g'

Constant Multiple Rule

(cf)'=c\times f'

The Number 'e'

\frac{d}{dx} e^{x}=e^{x}

The Product Rule

(fg)'(x)=f(x)g'(x)+g(x)f'(x)

The Quotient Rule

(\frac{f}{g})'(x) = \frac{g(x)f'(x)-f(x)g'(x)}{g(x)^{2}}

\frac{LO*HI' - HI*LO'}{LO*LO}

Average Rate of Change

\frac{\Delta y}{\Delta x}

Average Rate of Change

\frac{\Delta y}{\Delta x} = \frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}

Instantaneous Rate of Change

f'(x_{0})= \frac{\lim}{x_{1}> x_{2}} \frac

Instantaneous Rate of Change

f'(x_{0})= \frac{\lim}{x_{1}> x_{2}} \frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}

Height (motion under gravity)

s(t)=s_{0}+ v_{0}t +\frac{1}{2}gt^{2}

Velocity (under gravity)

v(t)=\frac{ds}{dx} = v_{0}-gt

\frac{d}{dx}\sin (x)=

\frac{d}{dx}\sin (x)= \cos(x)

\frac{d}{dx}\cos (x)=

\frac{d}{dx}\cos (x)=-\sin(x)

\frac{d}{dx}\tan(x)=

\frac{d}{dx}\tan(x)=\sec^{2}(x)

\frac{d}{dx}\sec (x)=

\frac{d}{dx}\sec (x)=\sec(x)\tan(x)

\frac{d}{dx}\cot (x)=

\frac{d}{dx}\cot (x)=-\csc^{2}(x)

\frac{d}{dx}\csc (x)=

\frac{d}{dx}\csc (x)= -\csc(x)\cot(x)

The Chain Rule

(f(g(x)))'=f'(g(x))*g'(x)

Generalized Power Rule

\frac{d}{dx}g(x)^{n}=n(g(x))^{n-1}*g'(x)

Shifting and Scaling Rule

\frac{d}{dx} f(kx+b)=kf'(kx+b)

\frac{d}{dx}\sin^{-1}(x)=

\frac{d}{dx}\sin^{-1}(x)=\frac{1}{\sqrt{1-x^{2}}}

\frac{d}{dx}\cos^{-1}(x)=

\frac{d}{dx}\cos^{-1}(x)=\frac{-1}{\sqrt{1-x^{2}}}

\frac{d}{dx}\tan^{-1}(x)=

\frac{d}{dx}\tan^{-1}(x)=\frac{1}{x^{2}+1}

\frac{d}{dx}\cot^{-1}(x)=

\frac{d}{dx}\cot^{-1}(x)=\frac{-1}{x^{2}+1}

\frac{d}{dx}\sec^{-1}(x)=

\frac{d}{dx}\sec^{-1}(x)=\frac{1}{|x| \sqrt{x^{2}-1}}

\frac{d}{dx}\csc^{-1}(x)=

\frac{d}{dx}\csc^{-1}(x)=\frac{-1}{|x| \sqrt{x^{2}-1}}

\frac{d}{dx}b^{x} =

\frac{d}{dx}b^{x} = (\ln{b})b^{x}

\frac{d}{dx}\ln{f(x)} =

\frac{d}{dx}\ln{f(x)} = \frac{f'(x)}{f(x)}

\frac{d}{dx}\ln{x}=

\frac{d}{dx}\ln{x} = \frac{1}{x}

\frac{d}{dx}\ln{x}=

\frac{d}{dx}\ln{x} = \frac{1}{x}

About this deck

Author: Elizabeth W.

Created: 2014-03-04

Updated: 2014-03-04

Size: 32 flashcards

Views: 6

Created: 2014-03-04

Updated: 2014-03-04

Size: 32 flashcards

Views: 6

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