(a) Explanation Given: The given function is g ( x ) = e f ( x ) , where f is a differential function. Formula used: The chain rule for exponential functions is, d d x ( e f ( x ) ) = e f ( x ) f ′ ( x ) Calculation: The derivative of given function g ( x ) is, (b) To determine To fill: The statement “If g ( x ) = ln f ( x ) where f is a differential function, then g ′ ( x ) = ____.”

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 5, Problem 8CRQ

(a)

To determine

To fill: The statement “If g(x)=ef(x) where f is a differential function, then g′(x)= ____.”

(b)

To determine

To fill: The statement “If g(x)=lnf(x) where f is a differential function, then g′(x)= ____.”

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Chapter 5, Problem 7CRQ

Chapter 5, Problem 9CRQ

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Chapter 5 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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The statement “If g ( x ) = e f ( x ) where f is a differential function, then g ′ ( x ) = ____.”

Solution Summary: The author explains that the derivative of given function g(x)=ef