derivative of x^x

derivative of x^x, calculus tutorial, logarithmic differentiation of x to the x power

0:00 first way, logarithmic differentiation, take ln both sides first
3:45 second way, write x as e^ln(x)

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[wesleydeng]

Moral: introduce e or ln when you have trouble differentiating.

[swerdkk]

Kids differentiate a constant.
Men differentiate x^x.
Legends integrate x^x.

[-tv]

bruh man is holding two markers in one hand and switching them like its nothing

[technoultimategaming]

Schools: x^3 + 3x^5

Intigrate and derive this funtion

Homework: derive x^x

Exam: intigrate and derive x^(ax^2+bx+c)

[RJN]

I believe this derivative should be in every calculus book.

Probably, one of the most beautiful (yet simple) derivatives ever... Good job, as always!

[PhysicsPhundamentals]

It's so cool to be studying calculus in school and finally start understanding these videos. Love it! Keep up the awesome work. :)

[derfret]

I once searched the lowest value of this function, long before i knew about calculus. Now can understand concretely, why x=1/e is the minimum of x^x. Thanks for this nice video!

[mistymouse]

Another why to do this is to use partial derivatives and the chain rule. (x^c)'=cx^(c-1) and (c^x)'=(c^x)ln c. Therefore, (x^x)'=x(x^(x-1)) + x^x (ln x) = x^x +x^x (ln x).

[wiiwillRule]

I watched this video, not because I had any studying to do, but just because I love your videos! You explain things so clearly and you obviously love mathematics (it's a bit contagious, apparently).

[sergiokorochinsky]

you can use a rule similar to the rule for multiplication:
derivative of the power (keeping the exponent constant) plus the derivative of the exponential (keeping the base constant).

y'= x x^(x-1) +x^x ln(x)
= x^x (1+ln(x))

[mariogabrielsalvatierrafra]

I've never seen such a crazy way to differentiate x^x
I mean, teachars never do something so amazing

[jacksoncasper]

“You can’t just bring the x down and do x^(x-1).”

[sad d/dx noises]

[FF-pvht]

ppl in the comments be like "I remember this from highschool" and im just sitting here thinking "I wish we did anything remotely advanced like this in highschool."
We literally just were given f'(x) must be this and that if f(x) is that, now compute that shit. The high point of knowledge was knowing why f'(x)=0 implies an extremum and how to confirm it

[JosaxJaz]

love this guy
answers all my random calc questions and seems like a genuinely chill dude

[emestella_]

OH MY GOD. OKAY.

I began the second way, thinking about e^(x ln(x)), but I have never thought about e^(x ln(x)) being simplified, so I ended up with another result which was correct but not as simple as yours. However, I had the right idea using e^ln(u), I have finally solved something before watching the solution. I doing better maths each days ! Thank you for sharing your passion of maths !

[meeranfakih]

I knew about the first method but second method was beautiful

[Kosekans]

Differentiation is mechanics, integration is art.

[gustavpeter]

This was on my math exam in my first year at Uni
It was taught in the one single lecture I missed

[kujmous]

So nonchalantly done, and I'm floored.