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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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Evaluating Logarithms In Exercises 23-28, evaluate the logarithm without using a calculator. See Example 8.

f ( x ) = l n 1 + e x 1 e x

To determine

To calculate: The derivative of the function f(x)=ln1+ex1ex.

Explanation

Given information:

The provided function is f(x)=ln1+ex1ex.

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

The derivative of function f(x)=un using the chain rule is,

f(x)=ddx(un)=nun1dudx

Where, u is the function of x.

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

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