Chapter 9.8, Problem 8E

### 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 7-12, find the third derivative. 8.   y = 6 x 3 − 12 x 2 + 6 x

To determine

To calculate: The third derivative of the function y=6x312x2+6x.

Explanation

Given Information:

The function is y=6x3âˆ’12x2+6x.

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=6x3âˆ’12x2+6x

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

dydx=ddx(6x3âˆ’12x2+6x)=ddx(6x3)âˆ’ddx(12x2)+ddx(6x)=6ddx(x3)âˆ’12ddx(x2)+6ddx(x)

Apply the power rule,

dydx=6(3â‹…x3âˆ’1)âˆ’12(2â‹…x2âˆ’1)

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