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Chapter 2: Q. 53 (page 222)
Use logarithmic differentiation to find the derivatives of each of the functions in Exercises 49–58.
The derivative of function is
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For each function f that follows find all the x-values in the domain of f for which and all the values for which does not exist in later section we will call these values the critical points of f
localid="1648604345877"
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
24.
Use the definition of the derivative to prove the following special case of the product rule
Stuart left his house at noon and walked north on Pine Street for minutes. At that point he realized he was late for an appointment at the dentist, whose office was located south of Stuart’s house on Pine Street; fearing he would be late, Stuart sprinted south on Pine Street, past his house, and on to the dentist’s office. When he got there, he found the office closed for lunch; he was minutes early for his appointment. Stuart waited at the office for minutes and then found out that his appointment was actually for the next day, so he walked back to his house. Sketch a graph that describes Stuart’s position over time. Then sketch a graph that describes Stuart’s velocity over time.
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
27.
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