Chapter 2: Q. 7 (page 221)
Explain how the formula for differentiating the natural logarithm function is a special case of the formula for differentiating logarithmic functions of the form
Short Answer
The reason has been explained.
Chapter 2: Q. 7 (page 221)
Explain how the formula for differentiating the natural logarithm function is a special case of the formula for differentiating logarithmic functions of the form
The reason has been explained.
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Get started for freeEach graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The line tangent to the graph of
Use the definition of the derivative to prove the following special case of the product rule
Every morning Linda takes a thirty-minute jog in Central Park. Suppose her distance s in feet from the oak tree on the north side of the park
(a) What was the average rate of change of Linda’s distance from the oak tree over the entire thirty-minute jog? What does this mean in real-world terms?
(b) On which ten-minute interval was the average rate of change of Linda’s distance from the oak tree the greatest: the first
(c) Use the graph of
(d) Approximate the times at which Linda’s (instantaneous) velocity was equal to zero. What is the physical significance of these times?
(e) Approximate the time intervals during Linda’s jog that her (instantaneous) velocity was negative. What does a negative velocity mean in terms of this physical example?
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