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14209an4.2-4

14209an4.2-4 - by R t = 20000 86 t What is the rate of...

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c ± Kendra Kilmer February 27, 2009 Section 4.2 - Derivatives of Exponential and Logarithmic Functions More Derivative Rules: If f ( x ) = e x then If f ( x ) = ln x then Example 1: Find the derivative of each of the following functions: a) f ( x ) = 2 e x b) g ( x ) = ln x + 7 c) h ( x ) = x 2 - 4 xe x + 9 x ln x x Example 2: Let’s look at how we would go about ﬁnding the derivatives of logs and exponential functions with other bases. 2

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c ± Kendra Kilmer February 27, 2009 Summary: Example 3: Find the derivative of each of the following functions: a) f ( x ) = 7 ( 5 ) x b) g ( x ) = ln ( x 7 )+ 3 ( 2 ) x c) h ( x ) = 4 x 2 - 3 x + log 7 x 3 - 5 x d) F ( x ) = ln 5 x 6 3
c ± Kendra Kilmer February 27, 2009 Example 4: The resale value R (in dollars) of a compnay car after t years is estimated to be given
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Unformatted text preview: by R ( t ) = 20000 ( . 86 ) t What is the rate of depreciation (in dollars per year) after 1 year? 3 years? Example 5: A mathematical model for the average of a group of people learning to type is given by N ( t ) = 10 + 9ln t , t ≥ 1 where N ( t ) is the number of words per minute typed after t hours of instruction and practice. a) What is the rate of learning after 1 hour of instruction and practice? b) What is the rate of learning after 10 hours of instruction and practice? Section 4.2 Homework Problems: 1,5,9,13,17,21,27,29,31,35,39,43,45 4...
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14209an4.2-4 - by R t = 20000 86 t What is the rate of...

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