Problem

Find the derivative of the function using the def…

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Problem 21 Easy Difficulty

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative.

$ f(x) = 3x - 8 $

Answer

$\lim _{h \rightarrow 0} \frac{3 h}{h}=\lim _{h \rightarrow 0} 3=3$

More Answers

02:28

Daniel J.

Topics

Limits

Derivatives

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

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Top Calculus 1 / AB Educators

Catherine R.

Missouri State University

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Campbell University

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Baylor University

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University of Nottingham

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Video Transcript

in this problem, we have F of X equals three x minus eight. The domain uh For dysfunction uh consists of all values of X for which dysfunction would be defined. Uh The domain basically is going to be all real numbers X can be any real number because dysfunction three times x minus eight will be defined for any real number. So the domain is to set up all real numbers where you can think of it as the entire X axis. Now the derivative of F with respect to X. F. Prime of X. If we differentiate our function F of X equals three X minus eight with respect to X, the derivative of three X is three. Ah the derivative of a constant is zero. So the derivative with respect to X F prime of X is three. The domain of this derivative function. Well, since it's equal to the constant three, regardless of what X is once again, X could be any real numbers. So the domain is the set of all real numbers or the entire X. Axis.

Leon D.

Temple University

Topics

Limits

Derivatives

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Top Calculus 1 / AB Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Caleb E.

Baylor University

Samuel H.

University of Nottingham