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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 85–98, find the derivative of the function.

y = ln x x 4

To determine

To calculate: The derivative of the function y=lnxx4.

Explanation

Given information:

The provided function is y=lnxx4.

Formula used:

Quotient rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f'(x)g(x)f(x)g'(x)[g(x)]2

Where, g(x)0.

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

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

ddx(un)=nun1dudx

Where, u is the function of x.

Calculation:

Consider the function, y=lnxx4

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