Unit 2 Derivatives

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general limit definition

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limh→0 (f(x+h) - f(x)) /h

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alternate limit definition

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limx→c (f(x) - f(c)) / (x-c)

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15 Terms

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general limit definition

limh→0 (f(x+h) - f(x)) /h

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alternate limit definition

limx→c (f(x) - f(c)) / (x-c)

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differentiability reqs:

  1. must be continuous

  2. no sharp turns or vertical tangents

  3. same derivative across a piecewise if needed

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constant rule

if f(x) = c, f’(x) = 0

since f(x) is a straight line, the derivative (slope) is zero

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power rule

if f(x) = xn , then f’(x) = n(x)n-1

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derivative of exponential functions

ex

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derivative of natural log functions

1/x

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d/dx sinx

cosx

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d/dx tan x

sec2x

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derivative of secx

secxtanx

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d/dx cosx

-sinx

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derivative of cotx

-csc2x

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d/dx cscx

-cscxcotx

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product rule f*g

h’(x) = f’(x)*g(x) + f(x)*g’(x)

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quotient rule f/g

h’(x) = (f’(x)g(x) - f(x)g’(x)) / g(x)2