Professor Walid Bouaichi: Derivative of Power and Linear Functions

Differentiation Rules: Power and Linear Function

When you hear the word “Derivative”, many things run through your mind. You may be wondering, What the heck is a “Derivative”? Plain and simple a “Derivative” is something that is based on another source. Speaking in Math Lingo, the “Derivative” is the instantaneous rate of change at a certain point. When you come across a Power Function or a Linear Function, you may decide to randomly take the First Derivative to see exactly how a point is on a graph is behaving. 

While I could be a cruel Professor and go ahead and introduce the long way of finding derivatives of points using the long way, I will just introduce two Differentiation Rules for evaluating the Derivative of Power and Exponential Functions. I do expect that who ever taught you before me explained finding the Derivative using Limit Approximation, which is seen below:

The Derivative Function can be written in multiple ways, for a function “f”, the  Derivative function, written as f’(x), is the instantaneous rate of change of “f” at “x”. The Derivative Function can also be written as “dy/dx”, which is known as Leibniz Notation. Leibniz was a smart guy, all that I will require you to know about his notation is that it relates the change in y with respect to the change in x.

Differentiating a Power Function

The first Differentiation rule that I will introduce to you is for Power Functions. Power functions, are pretty powerful, not as much as Superman but they are pretty powerful. 

A Power Function can be expressed as…… 

When taking the Derivative of a Power Function….

Multiply the power, “n”, by the “x-value” in the function and subtract 1 from the original n value in the power, this is your new power, n-1. 

Differentiating a Linear Function

The second Differentiation rule that I will introduce to you is for Linear Functions. Linear Functions, have a straight line when graphed, not curvy, or wavy, but straight. 

A Linear Function can be expressed as…. 

When taking the Derivative of a Linear Function……

The m-value in front of your x-variable is your derivative, deriving this will eliminate the x variable. If you have a constant, b, then the derivative of that will be 0.