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20 Cards in this Set

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  • Back
definition of a derivative
lim f(x+h)-f(x)
h->0 h
power rule
d/dx x^r= rx^(r-1)
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/√(1-x^2)
d/dx cos^-1x
-1/√(1-x^2)
d/dx tan^-1x
1/1-x^2
chain rule:
d/dx g(f(x))=

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