   Chapter 2.R, Problem 10E

Chapter
Section
Textbook Problem

# 10–11 Find f ' ( x ) from first principles, that is, directly from the definition of a derivative. f ( x ) = 4 − x 3 + x

To determine

To find: f'(x)

Explanation

1) Concept:

Definition of first derivative

2) Formula:

f'x=limh0fx+h-f(x)h

3) Given:

fx=4-x3+x

4) Calculation:

fx=4-x3+x

fx+h=4-(x+h)3+(x+h)

Substitute values of fx and fx+h in f'x=limh0fx+h-f(x)h

We get

f'x=limh04-(x+h)3+(x+h)-4-x3+xh

By multiplying (3+(x+h))(3+x) to numerator and denominator

We get

f'x=limh0(4-x+h)(3+x)-(4-x)(3+(x+h))(3+(x+h))(3+x)h

By solving it

f'x=limh012-3

### 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

#### Expand each expression in Exercises 122. (x+yxy)2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 1124, find the indicated limits, if they exist. 24. limxx2x+1

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

#### Multiply: 1520320

Elementary Technical Mathematics

#### Find the number n such that i=1ni=78.

Single Variable Calculus: Early Transcendentals

#### limnn2+3n2n2+n+1= a) 0 b) 12 c) 1 d)

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