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# The Derivative Function - Concept

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

By definition, the derivative is a function which is derived from another function. The definition of the derivative is usually only written for one point, but the function is defined for all points. **Derivative functions** of many kinds of functions can be found, including derivatives of linear, power, polynomial, exponential, and logarithmic functions.

I want to talk about the derivative function let's say we're looking at a function like f of x equals x squared plus 1. I have a graph here, in a previous example we found the derivative of this function at x equals 3 and we used the definition of the derivative and we got 6. Now it turns out you could do that at pretty much any point, you can find the derivative at negative 1, turns out to be negative 2 and you can find the derivative at a half and it turns out to be 1.

This function and many functions have derivatives at every value of x in their domain and so that gives us the notion of the derivative function. This f prime of x defines a function of x. For every value of x you think of you can come up with a derivative value. So that's a new function that we call the derivative function for f of x.

We're going to be talking about derivative functions for a while and the idea is that given a function you want to find it's derivative that is it's a derivative function and usually that means finding a formula for the derivative function that doesn't involve the limit, and that's what we're going to be doing in the next few episodes.

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###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

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