   Chapter 9.8, Problem 10E ### 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

# In Problems 7-12, find the third derivative. 10.   f ( x ) = 3 x 5 − x 6

To determine

To calculate: The third derivative of the function f(x)=3x5x6.

Explanation

Given Information:

The function is f(x)=3x5x6.

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 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,

f(x)=3x5x6

To find the first order derivative, differentiate both sides with respect to x,

f(x)=ddx(3x5x6)=ddx(3x5)ddx(x6)=3ddx(x5)ddx(x6)

Apply the power rule,

f(x)=3(5x51)(6x61)=15x46x5

To find the second order derivative, differentiate both sides with respect to x,

f

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