Chapter 9.8, Problem 2E

### 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 1-6, find the second derivative. 2.   y = 6 x 5 − 3 x 4 + 12 x 2

To determine

To calculate: The second derivative of the function y=6x53x4+12x2.

Explanation

Given Information:

The function is y=6x5âˆ’3x4+12x2.

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=6x5âˆ’3x4+12x2

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

dydx=ddx(6x5âˆ’3x4+12x2)=ddx(6x5)âˆ’ddx(3x4)+ddx(12x2)=6ddx(x5)âˆ’3ddx(x4)+12ddx

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