   Chapter 9.7, Problem 8E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the derivatives of the functions in Problems 1-32. Simplify and express the answer using positive exponents only. y = ( x 3 − 5 x 2 + 1 ) ( x 3 − 3 )

To determine

To calculate: The simplified form of the derivative of y=(x35x2+1)(x33).

Explanation

Given Information:

The function is y=(x35x2+1)(x33).

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the product rule, if f(x)=u(x)v(x), then

f(x)=u(x)v(x)+v(x)u(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

The derivative of a constant value, k, is

ddx(k)=0

Calculation:

Consider the provided function,

y=(x35x2+1)(x33)

Differentiate both sides with respect to x,

y=ddx((x35x2+1)(x33))

Simplify using the product rule,

y=(ddx(x35x2+1))(x33)+(ddx(x33))(x35x2+1)=(ddx(x3)ddx(5x2)+ddx(1))(x33)+(ddx(x3)ddx(

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