The derivative of e^x.

Description:
The derivative of e^x is....itself! e^x.

Learning Objectives
1) Compute the derivative of e^x

Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.

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[armonnaddaf]

“You could not live with your own derivative. And where did that take you? Back to e.”

[klausnordmeyer]

These lectures would be greatly enhanced if proofs were included, either in the lectures themselves or in an adjunct series of lectures.

[angelmendez-rivera]

This is somewhat unsatisfying, and I think that there needs to be an explanation as to why this exponential function is equal to its own derivative, and in particular, if one wants to define e to be equal to the unique real number t such that dt^x/dx = t^x is true, then one should prove that there are no other real numbers for which this equation is true, and then one needs to show that such a number is well-defined.

Of course, I also partly think this is a problem with context: the video already assumes you know what the number e is and what e^x is defined as for any real number x, but I think the problem is that, in general, teachers tend to omit the explanation for what e^x is, and in showing that this has a meaningful value.

[TheFacial]

I found your channel very helpful for me to self study in math. If you have time could you do some video about number theory thanks sir.

[sanjayghimire]

Thank you for the video. Your a ⭐ keep shining

[technoultimategaming]

And integral or area under e^x is also e^x

[vishalkumar-hugl]

So it's durutuvive not derivative