   Chapter 9.8, Problem 5E ### 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 1-6, find the second derivative. 5.   y = x 3 − x

To determine

To calculate: The second derivative of the function y=x3x.

Explanation

Given Information:

The function is y=x3x.

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=x3x

Rewrite the function using numeric value of powers,

y=x3x12

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

dydx=ddx(x3x12)=ddx(x3)ddx(x12)

Apply the power rule and rule of differentiating a constant,

dydx=(3x31)(12

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