   Chapter 3.2, Problem 14E

Chapter
Section
Textbook Problem

Differentiate. y = x 2 + 1

To determine

To find: The derivative of the function y=x2+x.

Explanation

Given:

The function y=x2+x.

Derivative rule:

(1) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddx[f1(x)]f1(x)ddx[f2(x)][f2(x)]2

(2) Power Rule: ddx(xn)=nxn1

(3). Sum rule: ddx(f+g)=ddx(f)+ddx(g)

Calculation:

The derivative of the function is g(x), which is obtained as follows.

dydx=ddx(y)=ddx(x2+x)=ddx(x122+x)

Substitute x12 for f1(x) and 2+x for f2(x) in the quotient rule (1),

dydx=(2+x)ddx[x12](x12)ddx[2+x][2+x]2

Apply the derivative rule (2) and (3) and simplify the terms,

dydx=(2+x)ddx[x12](x12)[ddx(2)+ddx(x)](2+x)2=(2+</

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