   Chapter 4.5, Problem 18E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Differentiating Logarithmic Functions In Exercises 1-22, find the derivative of the function. See Examples 1, 2, 3, and 4. y = ln ( 6 − x ) 3 / 2 x 2 / 3

To determine

To calculate: The derivative of the function y=ln(6x)32x23.

Explanation

Given information:

The provided function is y=ln(6x)32x23.

Formula used:

Let a be a positive real number a1 and u be a differentiable function of x. The derivative of natural logarithm of a function is,

ddx[logau]=(1lna)(1u)dudx

As with the natural logarithm function, if x and y are positive numbers such that x1 and y1 then lnxy=lnxlny.

As with the natural logarithm function, if x is a positive number such that x1 and y is a real number then lnxy=ylnx.

Calculation:

Consider the function, y=ln(6x)32x23

Apply the properties of logarithm,

y=ln(6x)32x2<

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