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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 = x 3 ln x ; ( e , e 3 )

To determine

To calculate: The equation of the tangent to the graph of the function y=x3lnx at the point (e,e3).

Explanation

Given information:

The function is y=x3lnx and the point is (e,e3).

Formula used:

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

Product 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)

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

ddx(un)=nun1dudx

Where, u is the function of x.

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

yy1=m(xx1)

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

Calculation:

Consider the function, y=x3lnx

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