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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 $

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02:28

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Missouri State University

University of Nottingham

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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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.

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