Derivative of the Lambert W function

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[teavea]

It's like you're deriving fast with a Lambertghini. (I'll show myself out.)

[sebastiansimon]

Also works with the formula for the derivative of the inverse: (f⁻¹)'(x) = 1 / f'(f⁻¹(x))

W'(x) = 1 / (xeˣ)' ∘ W(x) = 1 / (e^W(x) + x) = …

I think you’ve already shown this way in a previous video.

[deyomash]

I used implicitit differentiation. KNowing W(x) is the solution to x = y exp(y) <> y= W(x). I took d/dx on both sides, same story :) Cool!

[budoray]

This lesson was spoken so fast that I feel like I just bought a hundred head of cattle at a Texas auction house. Nice lesson.

[RomanSchelhorn]

First time coming across one of your videos... Perhaps the best math video I have ever seen in my life

[maxxie]

Amazing. I didn't think this function could have such nice identities.

[Debg]

If you include this on the T-shirt, I will definitely buy it!

[ligda_rudna_]

Great video as always! I like you to talk about the tetration, specially if u can generalise for negative values.
SPOILER:
a^^(0)=1
a^^(-1)=0
a^^(-2)~-∞.
a^^(-3)~∞.
And It continues at this way for the rest of negative integers.
Good luck ;)

[SyberMath]

Great work! Thank you for the inspiration for my most recent video! 😍💖

[pablojulianjimenezcano]

Yes pleaseee, add that derivative to your damn t-shirt!!

[alejrandom]

Cool! I took a try with implicit differentiation and got the same result :)

[mayankshah]

Sir, Please make a video on methods to calculate the value of Pi.

[baconboyxy]

Note that the simplified forms don’t work for x=0 because when doing the substitution for e^W(x) = x/W(x) this assumes that W(x) is not equal to 0, which is not true for W(0). In this case, W’(0) = 1 using the first form.

[adrianyaguar]

second form is wrong, does not work with 0 point. Even when you will find numerical solution for this differential equation you will get approx. -0.132 for x=0, which is wrong :) First form is perfect :) Amazing video, keep on! :)

[fsisrael]

Is there an algebric representation to w(x)? or is it just w(x) and thats it?

[annamma]

Can u make a video for proof of w function

[GreenMeansGOF]

If you leave your answer alone without doing the blue substitutions, then we can evaluate W’(0)=1. Note that your final answer is not valid for x=0. Now my question is: is it possible to evaluate the one-sided limits of the difference quotient at -1/e?

(W(h-1/e)+1)/h

It would be cool if you did a video on this.

[EmonsPlanet]

Me trying to learn something new of mathematics from the YouTube
BlackpenRedpen: Let's differentiate that

[Pritzelita]

I’m not very familiar with the Lambert function, but is it possible to write it in terms of x?

[rah]

Maybe you need a second Tshirt with D and anti D of Lambert function, Error function, Gamma function and other cool functions like that?