   Chapter 3.2, Problem 7E

Chapter
Section
Textbook Problem

Differentiate. g ( x ) = 1 + 2 x 3 − 4 x

To determine

To find: The differentiation of the function g(x)=1+2x34x.

Explanation

Given:

The function g(x)=1+2x34x.

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)

(4) Constant multiple rule: ddx(cf)=cddx(f)

(5) Difference rule: ddx(fg)=ddx(f)ddx(g)

Calculation:

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

g(x)=ddx(g(x))=ddx(1+2x34x)

Substitute 1+2x for f1(x) and 34x for f2(x) in the quotient rule (1),

g(x)=(34x)ddx[1+2x](1+2x)ddx[34<

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