   Chapter 11.1, Problem 4CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find f ' ( x )  for  f ( x ) = l n [ 2 x 4 ( 5 x + 7 ) 5 ] .

To determine

To calculate: The derivative f(x) of the function f(x)=ln[2x4(5x+7)5].

Explanation

Given Information:

The provided function is f(x)=ln[2x4(5x+7)5].

Formula Used:

The quotient rule for any positive numbers M and N, lnMN=lnMlnN.

The power rule for any positive number M is such that, lnMp=plnM, where p is any real number.

Derivative of natural logarithmic functions is such that, if y=lnu, where u is a differentiable function of x then dydx=1ududx.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

Calculation:

Consider the function, f(x)=ln[2x4(5x+7)5]

Use quotient rule for logarithms,

f(x)=ln(2x4)ln(5x+7)5

Use power rule for logarithms,

f(x)=ln<

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