   Chapter 9.8, Problem 7E ### 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. 7.   y = 6 x 5 − 16 x 3 + 12

To determine

To calculate: The third derivative of the function y=x516x3+12.

Explanation

Given Information:

The function is y=x516x3+12.

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,

y=x516x3+12

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

dydx=ddx(x516x3+12)=ddx(x5)ddx(16x3)+ddx(12)=ddx(x5)16ddx(x3)+ddx(12)

Apply the power rule and rule of differentiating a constant,

dydx=(5x51)16(3x31)+0=5x

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 