Derivative Involving Exponential

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Derivative Involving Exponential Logarithmic
Functions
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Formulas

• Let a be a positive number other than one. Then
• 1. f(x) ax ? f' (x) ax lna
• Special Case f(x) ex ? f' (x) ex
• 2. f(x) logax ? f' (x) (1/x) (1/lna)
• Special Case f(x) lnx ? f' (x) 1/x

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Examples
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General FormulasChain Rule

• Let a be a positive number other than one. Then
• 1. f(x) au(x) ? f'(x) au(x) lna . u' (x)
• Special Case
• f(x) eu(x) ? f' (x) eu(x) . u' (x)
• 2. f(x) logau(x) ?f' (x) (1/u(x)) (1/lna) u'
  (x)
• Special Casef(x) lnu(x) ? f' (x) 1/u(x) .
  u' (x)

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Examples Find f(x)
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Solution
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Exercises Find f(x)