Chapter 2: Q. 65 (page 234)
Use logarithmic differentiation to find the derivative of given function
Short Answer
The derivative of given function is
Chapter 2: Q. 65 (page 234)
Use logarithmic differentiation to find the derivative of given function
The derivative of given function is
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Get started for freeUse the definition of the derivative to find for each function in Exercises 39-54
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A tomato plant given ounces of fertilizer will successfully bear pounds of tomatoes in a growing season.
(a) In real-world terms, what does represent and what are its units? What does represent and what are its units?
(b) A study has shown that this fertilizer encourages tomato production when less than ounces are used, but inhibits production when more than ounces are used. When is positive and when is negative? When is positive and when is negative?
In Exercises 69–80, determine whether or not is continuous and/or differentiable at the given value of . If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
Last night Phil went jogging along Main Street. His distance from the post office t minutes after p.m. is shown in the preceding graph at the right.
(a) Give a narrative (that matches the graph) of what Phil did on his jog.
(b) Sketch a graph that represents Phil’s instantaneous velocity t minutes after p.m. Make sure you label the tick marks on the vertical axis as accurately as you can.
(c) When was Phil jogging the fastest? The slowest? When was he the farthest away from the post office? The closest to the post office?
Prove, in two ways, that the power rule holds for negative integer powers
a) by using the definition of the derivative
b) by using thedefinition of the derivative
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