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

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Chapter 4.5, Problem 48E
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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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Finding an Equation of a Tangent Line In Exercises 45-52, find an equation of the tangent line to the graph of the function at the given point. See Example 5.

y = ln   x x 4 ;   ( e , 1 e 4 )

To determine

To calculate: The equation of the tangent to the graph of the function y=lnxx4 at the point (e,1e4).

Explanation

Given information:

The function is y=lnxx4 and the point is (e,1e4).

Formula used:

Let u be a differentiable function of x then, ddx[lnx]=1x,x>0 and ddx(lnu)=1ududx,u>0.

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

ddx(un)=nun−1dudx

Where, u is the function of x.

Equation of line passes through the point (x1,y1) is given as,

y−y1=m(x−x1)

Where, m is the slope and m=dydx at (x1,y1).

Calculation:

Consider the function, y=lnxx4

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