Chapter 9.6, Problem 15E

### 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

# 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=nunâˆ’1â‹…dudx, where u is a differentiable function of x.

Power of x rule for function f(x)=xn is fâ€²(x)=nxnâˆ’1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

If any nonzero real number a has a negative integer n as its exponent then aâˆ’n=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,

yâ€²=ddx(u1/2)

Use the power rule,

yâ€²=(12â‹…u12âˆ’1â‹…dudx)=12uâˆ’1/2dudx

Substitute (3x2+4x+9)<

### 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

## Additional Math Solutions

#### In Exercises 21-24, find the distance between the given points. 24. (2, 1) and (10, 6)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Evaluate the indefinite integral. 2t2t+3dt

Single Variable Calculus: Early Transcendentals, Volume I

#### True or False: If h(x) = g(x) for all x a and limxah(x)=L, then limxag(x)=L.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Graph each function. y=x-1

College Algebra (MindTap Course List)