   Chapter 8.4, Problem 4SWU ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# In Exercises 1-4, find the derivative of the function. g ( x )   =   2 x x 2   +   5

To determine

To calculate: The derivative of the function g(x)=2xx2+5.

Explanation

Given Information:

The provided function is g(x)=2xx2+5.

Formula used:

General power rule of differentiation:

ddx[xn]=nxn1

Quotient rule of differentiation:

ddx[a(x)b(x)]=b(x)a(x)a(x)b(x)[b(x)]2

The sum and difference formula of differentiation:

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

Calculation:

Consider the provided function is,

g(x)=2xx2+5

Apply the quotient rule of differentiation.

g(x)=(x2+5)ddx[2x]2xddx[x2+5](x2+5)2

Apply the sum and difference formula of differentiation to find the derivative of the above function.

(x2+5)ddx[2x]2xddx[x2+5](x2+5)2=(x2+5)ddx[2x]2x(ddx[x2]+ddx)(x2+5)2

Factor out the real numbers and substitute ddx=0 in the above function

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