The Proof - Why Does d/dx (x^n) = nx^(n-1) , Part 4

This the fourth video of a four part playlist. The first three videos briefly explain the math needed for the proof. This video provides a proof based on the math that was outlined in parts 1, 2 and 3.

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[jimmyhaotran]

The reason why you need to work out with simplifying the equation is so that you wont be dividing into zero, which is "illegal" but acceptable if you do it with limits and find a way to get rid of denominator by factorising it out first. Hope that helps

[hasanmahboobrahil]

excellent day realy we have after seeing this. very simple and effective way without any hustle to make people understand. I love your way of making us understand the facts behind formulae.

[harsha]

OH MY GOD I

Our Physics teacher just gave us this formula and said the derivation was very complex and we could google it if we wanted, and I did and after AN HOUR finally found this masterpiece :)

The derivation is still complex, but damn you did it well

[tzakl]

for people who asked, h=change in x, because we you derivatives to measure a point, but how? Y/x=0/0???!!! Actually we use the formula f(x+change x)-f(x). While the f(x) is the slope of the point which you find by adding two points on both sides of the point you're working with. So there is no space actually, so afterwards after simplifying as much as possible, you have to actually shrink change of x to zero, or in other words Shrink h to zero, but you have to simplify as much as possible first. (I'm not the guy who made the video if you wonder) hope that helps

[omsushantkarki]

please tell me from where did the  ' h ' came from?
and how is d f(x)\dx = ( f(x+h)+f(x) )\h  ???

[joeverzino]

A little graph showing two tangent lines, one at x1 and one at x1+h.
Let h be a little large so you show two distinct tangents one at x1 and one at x1+h. Hold x1 the tangent at x1 still
and move the tangent at x1+h closer as h gets smaller.
Pictorially keep shrinking h until the 2 tangent lines are almost equal to the tangent at x1.

[joeverzino]

Hold the tangent at x1 still and move the tangent at x1+h slowly closer as h gets smaller.

[vaibhavchhaya]

Very nice explanation.
Btw can you prove the chain rule using composition of two functions?

[harishreddykadapala]

Firstly why you take limit is 0 and rhs function in right side why you take only that function

[alonwolf]

Thank you very much!
I hope you'll keep making videos, I learn a lot from them (:

[testself]

What will happen when n i s an irrational Please answer me

[pravatranjannayak]

Thank you sir it is very much helpful 😊

[dhruw]

Math is beautiful sometimes but other times its a nightmare

[obocchamakunobo]

Is there any other way in which I can prove this theorem without using the binomial theorem?

[SaniyaKhan-xswz]

Thank you so much sir... It really helpful

[fruityfan]

Thanks a million for this explanation 💜

[donzpicazo]

why does my cal. book say n! for answer to same prob??

[pravinmaske]

wow ! dude ..thnx alot ;) it ws vry helpful :D

[richardcommins]

This video is very amateurish and at best confusing. Draw a simple graph of a curve and place a dot at (x, y) where you want the derivative. Draw a tangent line from x and delta x. Now let delta x approach zero. Then we get the formula of the slope of the line as m = (y2-y1)/(x2-x1) or (F(x+dx) - F(x))/(dx) and take the limit as dx approaches zero. (no symbol for delta x) What is with this h that comes out of no where.

[Gothmilker]

Can anyone tell me what is d/dx of x^(n^n)