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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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In Exercises 9 and 10, find the slope of the graph of the function at the point (2, 4).

g ( x ) = x x 2 x + 2

To determine

To calculate: The slope of the graph of the function g(x)=xx2x+2 at the point (2,4).

Explanation

Given information:

The provided function is g(x)=xx2x+2 and the point is (2,4).

Formula used:

According to the product rule of differentiation, the derivative of the product of the two differentiable functions is equal to the first function with derivative of the second function plus the second function with derivative of the first function.

ddx[f(x)g(x)]=f(x)g(x)+g(x)f(x)

Calculation:

Consider the provided function is,

g(x)=xx2x+2

Apply the product rule derivative the function, g(x)=xx2x+2.

g(x)=(x)ddx(x2x+2)+(x2x+2)ddx(x)=(x)(12x2x+2(2x1))+(x2x+2)(1)=2x2x2x2x+2+x2x+2=2x2x+2(x2x+2)2x2x+2

Further solve the above derivative

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