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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

Differentiate.

f(x) = (3x2 – 5x)ex

To determine

To find: The differentiation of the function f(x)=(3x25x)ex.

Explanation

Given:

The function f(x)=(3x25x)ex.

Derivative rule:

(1) Product Rule: If f(x) and g(x) are both differentiable, then

ddx[f(x)g(x)]=f(x)ddx[g(x)]+g(x)ddx[f(x)]

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

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

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

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

Calculation:

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

f(x)=ddx(f(x))=ddx[(3x25x)ex]

Substitute 3x25x for f(x) and ex for g(

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