AP Calculus BC - Derivatives

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23 Terms

1
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definition of a derivative

lim h=0 (f(x+h)-f(x))/h

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ax

a

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constant

0

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x^n

nx^n-1

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cx^n

(cn)x^n-1

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sinx

cosx

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cosx

-sinx

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tanx

sec²x

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cscx

-cscxcotx

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secx

secxtanx

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cotx

-csc²x

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arccos

-1/sqrt(1-x²)

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arcsin

1/sqrt(1-x²)

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arctan

1/(1+x²)

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arcsec

1/(|x|sqrt(x²-1))

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arccsc

-1/(|x|sqrt(x²-1))

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arccot

-1/(1+x²)

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ax

1/(alnx)

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lnx

1/x

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f(x)+g(x)

f’(x)+g’(x)

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f(x)-g(x)

f’(x)-g’(x)

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f(x)g(x)

f’(x)g(x)+g’(x)f(x)

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f(x)/g(x)

g(x)f’(x)-f(x)g’(x)/(g(x)²)