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20 Cards in this Set
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definition of a derivative

lim f(x+h)f(x)
h>0 h 

power rule

d/dx x^r= rx^(r1)


how can a derivative NOT exist

1) discontinuities (jump, hole)
2) kink/sharp edge 3) vertical tangent (x^1/3 at x=0) 

sums of derivatives

d/dx( (f(x) + g(x) ) =
d/dx f(x) + d/dx g(x) 

product rule:

f'(x)g(x) + g'(x)f(x)


quotient rule

d/dx f(x)/g(x)=
g(x)f'(x) (f(x)g'(x)) g(x)^2 

d/dx sinx

cosx


d/dx cosx

sinx


d/dxtanx

sec^2x or 1/cos^2x


d/dx secx

secxtanx


d/dx cscx

cscxcotx


d/dx cotx

csc^2x


d/dx a^x

loga(a^x)
*****log is BASE e 

d/dx log x
a 
(1/loga)(1/x)


d/dx logx

1/x


d/dx e^x

e^x


d/dx sin^1x

1/√(1x^2)


d/dx cos^1x

1/√(1x^2)


d/dx tan^1x

1/1x^2


chain rule:

d/dx g(f(x))=
g'(f(x)) * f'(x) 