   Chapter 3.2, Problem 52E

Chapter
Section
Textbook Problem

If f is a differentiable function, find an expression for the derivative of each of the following functions.(a) y = x2f(x)(b) y = f ( x ) x 2 (c) y = x 2 f ( x ) (d) y = 1 + x f ( x ) x

(a)

To determine

To find: The expression for the derivative of the function y=x2f(x).

Explanation

Given:

The function is y=x2f(x).

Derivative rule:

(1) Product Rule: ddx[f1(x)f2(x)]=f1(x)ddx[f2(x)]+f2(x)ddx[f1(x)]

(2) 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)][f2x]2

(3) Power rule: ddx(xn)=nxn1

(4) Sum rule: d<

(b)

To determine

To find: The expression for the derivative of the function y=f(x)x2.

(c)

To determine

To find: The expression for the derivative of the function y=x2f(x).

(d)

To determine

To find: The expression for the derivative of the function y=1+xf(x)x.

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