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Derivative Involving Exponential & Logarithmic Functions

Derivative Involving Exponential & Logarithmic Functions. Formulas. Let a be a positive number other than one. Then: 1. f(x) = a x → f' (x)= a x lna Special Case: f(x) = e x → f' (x)= e x 2. f(x) = log a x → f' (x)= (1/x) (1/lna) Special Case: f(x) = lnx → f' (x)= 1/x. Examples.

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Derivative Involving Exponential & Logarithmic Functions

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  1. Derivative Involving Exponential & Logarithmic Functions

  2. 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

  3. Examples

  4. 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 Case:f(x) = lnu(x) → f' (x)= 1/u(x) . u' (x)

  5. Examples: Find f‘(x)

  6. Solution

  7. Exercises: Find f‘(x)

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