   Chapter 9.6, Problem 15E Mathematical Applications for the ...

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

Solutions

Chapter
Section Mathematical Applications for the ...

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

Differentiate the functions in Problems 3-20. y = 3 x 2 + 4 x + 9

To determine

To calculate: The derivative of the function y=3x2+4x+9.

Explanation

Given Information:

The provided function is y=3x2+4x+9.

Formula used:

Power rule for a real number n is such that, if y=un then dydx=nun1dudx, where u is a differentiable function of x.

Power of x rule for function f(x)=xn is f(x)=nxn1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

If any nonzero real number a has a negative integer n as its exponent then an=1an.

Calculation:

Consider the function, y=3x2+4x+9

Rewrite the function as,

y=(3x2+4x+9)1/2

Consider (3x2+4x+9) to be u,

y=u1/2

Differentiate both sides with respect to x,

y=ddx(u1/2)

Use the power rule,

y=(12u121dudx)=12u1/2dudx

Substitute (3x2+4x+9)<

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