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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 4, Problem 93RE
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Calculus: An Applied Approach (Min...

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Ron Larson
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Differentiating Logarithmic Functions In Exercises 85–98, find the derivative of the function.

y = ln x 2 x + 1

To determine

To calculate: The derivative of the function y=ln(x2x+1).

Explanation

Given information:

The provided function is y=ln(x2x+1).

Formula used:

The property of logarithms for the expression ln(xy) is ln(xy)=lnx−lny where x and y are real numbers greater than 0.

The property of logarithms for the expression lnxn is lnxn=nlnx where x and y are real numbers greater than 0.

Constant multiple rule of derivative of function f(x) is f'(cx)=cf'(x) where c is constant.

The derivative of natural logarithm of a function is ddxlnu=1ududx, where u is a differentiable function of x.

The derivative of natural logarithm of x is ddxlnx=1x.

Calculation:

Consider the function, y=ln(x2x+1).

Apply the property of ln(xy) as,

y=ln(x2)−ln(x+1)

Now, apply the property of lnxn as,

y=2lnx−ln(x+1)

Then, the derivative of the function is,

y′=ddx[2lnx−ln(x+1)]=ddx(2lnx)−ddx[ln(x+<

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Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-3CPSect-4.1 P-4CPSect-4.1 P-5CPSect-4.1 P-1SWUSect-4.1 P-2SWUSect-4.1 P-3SWUSect-4.1 P-4SWUSect-4.1 P-5SWU
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In Exercises 57 and 58, solve the given system of equations. 1x+1y1z=3 4x1y+5z=29 2x+2y3z=3 Hint: Put u=1x, v=1...

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