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4.4 and 4.5: Derivatives of Exponential and Log Functions. Review Properties of Logs and Exponential Function. Inverse: log a x = y a y = x l nx = y e y =x Other properties: ln a x = xlna l oga x = xloga. Properties of Logs and Exponential Functions cont.
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Review Properties of Logs and Exponential Function Inverse: logax = y ay = x lnx = y ey=x Other properties: ln ax = xlna logax= xloga
Properties of Logs and Exponential Functions cont. logaax=x lnex = x =x elnx = x Change of base: logax =
Derivative of ex: Derivative of ax:
Examples: Find the derivative. 1. 2. 3. 4.
Find the derivative. 1. 2. 3. 4.
1. 2.
When does the tangent line to the graph of y = 2t -3 have a slope of 21?
Find the derivative. 1. 2. 3. 4.
An absolute value inside of a logarithm has no effect on the derivative, other than make the result valid for more x values. (see p. 287) Example: Find the derivative.