Chapter 9.8, Problem 17E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 13-24, find the indicated derivative.Find d 4 y d x 4  if  y = 4 x 3 − 16 x .

To determine

To calculate: The value of d4ydx4 for the function, y=4x316x.

Explanation

Given Information:

The provided function is y=4x3âˆ’16x.

Formula used:

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

fâ€²(x)=nxnâˆ’1

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

gâ€²(x)=cfâ€²(x)

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

fâ€²(x)=uâ€²(x)+vâ€²(x)

The derivative of a constant value, k, is

ddx(k)=0

Calculation:

Consider the provided function,

y=4x3âˆ’16x

In order to get dydx differentiate both sides with respect to x,

dydx=ddx(4x3âˆ’16x)=ddx(4x3)âˆ’ddx(16x)=4ddx(x3)âˆ’16ddx(x)

Apply the power rule of derivatives,

dydx=4(3â‹…x3âˆ’1)âˆ’16(x1âˆ’1)=12x2âˆ’16

To find the value of d2ydx2, differentiate both

### 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