   Chapter 3.2, Problem 16E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Differentiate. y = 1 t 3 + 2 t 2 − 1

To determine

To find: The differentiation of the function y=1t3+2t21.

Explanation

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 y=1t3+2t21 is dydt, which is obtained as follow,

dydt=ddt(y)=ddt(1t3+2t21)

Apply the quotient rule (1),

dydt=[(t3+2t21)ddt(1)][(1)ddt(t3+2t21)](t3+2t21)2

Apply the derivative rules (3), (4), and (5),

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