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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 1-22, find the derivative of the function. See Examples 1, 2, 3, and 4.

y = ln x + 1 x 1

To determine

To calculate: The derivative of the function y=lnx+1x1.

Explanation

Given information:

The provided function is y=lnx+1x1.

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=lnx+1x1

Apply the properties of logarithm,

y=lnx+1x1=ln(x+

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