Explanation Logarithmic differentiation is a method used to obtain the derivative of the function by taking log on both side of the equation. For a function y = g ( x ) , the logarithmic differentiation is ln | y | = ln | g ( x ) | . It is simplified as ln | y | = ln | g ( x ) | 1 y ⋅ d y d x = g ′ ( x ) g ( x ) d y d x = y ⋅ g ′ ( x ) g ( x ) Logarithmic differentiation is used to differentiate certain functions. The derivative of a log is given below. d d x ( log x ) = 1 x The steps to obtain the derivative using logarithmic method are given below. Take the natural log of both sides of the equation. Differentiate the function with respect to x

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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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 3 Solutions

Calculus

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The procedure for logarithmic differentiation .

Solution Summary: The author explains how logarithmic differentiation is used to obtain the derivative of a function by taking log on both sides of the equation.

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Chapter 3 Solutions