Explanation Given: The function is, y = 3 x (1) Calculation: Take natural logarithm on both the sides of the equation (1). ln y = ln 3 x ln y = x ln 3 [ ∵ ln m n = n ln m ] Differentiate both sides of above equation with respect to x , d d x ( ln y ) = d d x ( x ln 3 ) In the left side of above equation, y is a function of x so take y = f ( x ) to change the variable in term of x , d d x ln [ f ( x ) ] = ln 3 ( d d x x ) 1 f ( x ) ⋅ d d x f ( x ) = ln 3 ( 1 )

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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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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Chapter 5.5, Problem 47E

To determine

To find: The derivative of the function y=3x .

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Chapter 5.5, Problem 46E

Chapter 5.5, Problem 48E

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Chapter 5 Solutions

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

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The derivative of the function y = 3 x .

Solution Summary: The author explains how to find the derivative of the function y=3x.

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