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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) If f(x) = (x3x)ex, find f'(x).

(b) Check to see that your answer to part (a) is reasonable by comparing the graphs of f und f'.

(a)

To determine

To find: The derivative of the function f(x)=(x3x)ex.

Explanation

Given:

The function f(x)=(x3x)ex.

Derivative rules:

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

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

(3) Difference Rule: ddx[f(x)g(x)]=ddx(f(x))ddx(g(x))

(4) Natural exponential function: ddx(ex)=ex

Calculation:

The derivative of f(x) is f(x), which is obtained as follows,

f(x)=ddx(f(x)) =ddx((x3x)ex

(b)

To determine

To check: The derivative f(x), f(x) is reasonable by comparing the graph of f(x) and f(x).

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