What is a Derivative? Deriving the Power Rule

After discussing differentiation at great length, it is time to connect this concept with the act of taking the derivative of a function. In actuality these mean the same thing, but using the power rule to take the derivative of a function is actually much simpler than all that business with limits and tangent lines! But it is important to know what the power rule is and where it comes from, so let's derive it together. This way, when you take the derivatives of functions, you'll know exactly what is really happening.

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[TheKarstrasse]

I was never taught like this in school because even our teachers didn't know all these. We directly started with dy/dx without understanding what they mean.

Thanks professor Dave. I'm a software application design architect since a couple years and still watching this now

[sujitsuram]

I don't know why but i like it when you give pauses between statements, helps me sync in a bit. Appreciate the work you have done so far.

[tasnimulsarwar]

Never, like never in my life have I ever been taught the preliminary of the derivative like this way. Never thought I would understand how we get to the power rule.
Thank you so much for this. This and your awesome and kindhearted work will always remain in my heart till the end of my days.
Once again, thank you so much.

[gr]

I have always appreciated how beautifully one can understand physics when you derive the equations instead of only memorizing them. One can understand the true meaning of those equations. You just did that for me with derivatives. I have watched countless videos, many very good, but yours is the first one I remember explaining where the power rule comes from. Just beautiful!

[kafkaesquegoku]

PROFESSOR DAVE THIS VIDEO LITERALLY CHANGED THE WAY I VIEW CALCULUS THANK U SO MUCH 😭😭😭 seeing the difference quotient being visualized changed

[furyplayer]

this professor just took the entire 1 week of calculus in just 10minutes video... Godbless you sir for making these videos

[DaReelGamerz]

Teachers these days should learn from Prof. Dave. I've never seen a clearer explanation of derivatives.
Finally understood calculus.
THX❤

[abhisheksingh-qvel]

After seeing this I think in India only focus is on how to put values on formula... many teachers actually don't know why they are doing so...
You are doing great job..keep it up sir

[igotapochahontas]

Best explaination for WHY the derivitive of a constant is zero ive ever seen. This is quickly becoming one of my favorite calculus channels. Have you considered doing some practical, easy, applied calculus videos? Everyone seems to dodge that subject. Id like to see some simple applications of calculus without having to bore myself to sleep with endless strings of algebra.

[kripashankarshukla]

Your explanation is of god level this is definitely the best calculus tutorial in the world I am very lucky to get it

[vinitsunita]

I am 32 years old and first time in my life I actually understood what power rule is and what is the application of differentiation. This is amazing video

[bd_ART]

Just As always, the best courses in the world

[gokucrafter]

You ARE one of BEST mentors that I have ever seen in my entire life. Even if I can ask questions with my teacher in class, I can't understand the definition to such a great degree, regardless of the fact that English is not my mother tongue.

[randoshmuckarias]

Thanks a lot Professor Dave! you really helped me understand it better. Since in our schools they simply make us memorize that the derivative of a number is 0 and the power rule and so on directly.

[lananhtran]

All these years I always thought Calculus is something really big and complicated but turns out it's just a fancier Algebra. And again, thank you, this is the best Calculus tutorial I've ever had.

[wendykurniawan]

thank you so much for explaining this. The best explanation of derivatives. All these years and at last someone can explain the logic behind derivatives. My teacher back then only gave me the formula without explaining further.

[metayoutubeacademy]

I just cried of joy, how easy you made my life, Love You Professor Dave

[KxGXRish_Gaming]

You are a great teacher please keep creating content... im from india and trying for iit jee exams and your explanation helped me a enhanced my basic would say that my proffessors dont even know this much about calculus...thanks to you

[kamidelstudio]

How does someone make calculus entertaining?!? Thank you for your videos

[Kiky_MedPhysicist]

Thank you sir for your dedication and for making this free!