ch.11.pdf - Chapter 11 11.1 Derivative of Logarithmic...

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Chapter 11 11.1 Derivative of Logarithmic Functions 1. Find derivative of the following functions: i. y = x 3 + 3 lnx ii. y = x 2 lnx 2. Find derivative of the following functions: i. f ( x ) = ln ( x 4 3 x + 7) ii. f ( x ) = 1 3 ln (2 x 6 3 x + 2) iii. g ( x ) = ln (2 x + 1) 2 x + 1 iv. f ( x ) = lnx 6 3. Use logarithm properties to find derivative of the following functions: i. f ( x ) = ln [ x ( x 5 2) 10 ] ii. f ( x ) = ln 3 3 x + 5 x 2 + 11 4 iii. f ( x ) = ln 2 x 4 (5 x + 7) 5 4. Suppose the cost function for x skateboards is given by: C ( x ) = 18 , 250 + 615 ln (4 x + 10) , where C ( x ) is in dollars. Find the marginal cost when 100 units are produced, and explain what it means. 5. Change-of-Base: Given y = log 4 ( x 3 + 1) , find dy dx . 6. Let: f ( x ) = xlnx x . Use graph of the derivative of f ( x ) for x > 0 to answer the following questions: i. At what value x = a , the graph of f ( x ) crosses the x-axis. ii. What value of x = a , is the critical value for f ( x ) . iii. Does f ( x ) have a relative maximum or a relative minimum at the critical value: x = a ? 11.2 Derivative of Exponential Functions 7. Find derivative of the following functions: i. y = 4 e x + 5 x 2 2 ii. f ( x ) = e 4 x 3 iii. s ( t ) = 5 te 3 t 2 +4 t iv. u = w e 7 w 8. Find derivative of the function:
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  • Fall '15
  • JasonChan
  • Derivative, Mathematical analysis, Logarithm, following functions

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