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20 Cards in this Set
- Front
- Back
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definition of a derivative
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lim f(x+h)-f(x)
h->0 h |
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power rule
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d/dx x^r= rx^(r-1)
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how can a derivative NOT exist
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1) discontinuities (jump, hole)
2) kink/sharp edge 3) vertical tangent (x^1/3 at x=0) |
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sums of derivatives
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d/dx( (f(x) + g(x) ) =
d/dx f(x) + d/dx g(x) |
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product rule:
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f'(x)g(x) + g'(x)f(x)
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quotient rule
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d/dx f(x)/g(x)=
g(x)f'(x)- (f(x)g'(x)) g(x)^2 |
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d/dx sinx
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cosx
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d/dx cosx
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-sinx
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d/dxtanx
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sec^2x or 1/cos^2x
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d/dx secx
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secxtanx
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d/dx cscx
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-cscxcotx
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d/dx cotx
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-csc^2x
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d/dx a^x
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loga(a^x)
*****log is BASE e |
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d/dx log x
a |
(1/loga)(1/x)
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d/dx logx
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1/x
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d/dx e^x
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e^x
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d/dx sin^-1x
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1/√(1-x^2)
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d/dx cos^-1x
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-1/√(1-x^2)
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d/dx tan^-1x
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1/1-x^2
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chain rule:
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d/dx g(f(x))=
g'(f(x)) * f'(x) |
