   Chapter 11.1, Problem 23E ### 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 d y d x if  y = ln ( x 3 x + 1 ) .

To determine

To calculate: The value of dydx for the function y=ln(x3x+1).

Explanation

Given Information:

The provided function is y=ln(x3x+1).

Formula Used:

The product rule for any positive numbers M and N, lnMN=lnM+lnN.

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

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).

If the logarithmic equation is y=lnx then its derivative is such that, dydx=1x.

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

Calculation:

Consider the function, y=ln(x3x+1)

Use product rule for logarithms,

y=lnx3+lnx+1=lnx3+ln(x+1)1/2

Use power rule for logarithms,

y=3lnx+12ln(x+1)

Differentiate with respect to

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