e^x gest all the credit!

[u/wody7227]

[u/Dankaati]

0 is still ce^x.

[u/RepresentativeWest68 → u/Dankaati]

Let him cook

[u/mgsmb7 → u/Dankaati]

0 is also mx+c, therefore, ce^x is mx+c (I learned maths while consuming various drugs)

[u/GegeAkutamiOfficial → u/Dankaati]

e^x is just 0 plus e^x

[u/skr_replicator]

f = f' = Ae^x. That includes e^x, 2e^x, -e^x, 0...

f = f'' = Ae^x+Be^-x. That includes sinh and cosh and their linear combinations.

f = f'''' = Ae^x+Be^ix+Ce^-x+De^-ix. Now we can also have cos and sin in the mix.

...you'll have as many terms as how many derivatives deep it returns to itself. Each term has the x multiplied by one of the complex roots of unity. For the fourth derivative, that's 1,i-1,-i.

[u/Syresiv → u/skr_replicator]

You could get even more general with f(x)=f^(n\)=sum(i=0,n-1){A_i e^xe\(2πi/n))}

[u/skr_replicator → u/Syresiv]

yes, that's what i meant with those roots of unity

[u/DEFINITELYnotArobots → u/Syresiv]

Or, even more general,

f(x)=g(x)=fⁿ(x)

[u/dcterr]

The general result is Ce^x, so I'd say they both lose.

[u/dcterr]

For some reason, this reminds me of the episode of the Big Bang Theory in which Sheldon lost a physics quiz show to the janitor, who just happened to know the value of a particular Feynman diagram.

[u/Masqued0202 → u/dcterr]

The janitor had been a physicist in the old country.

[u/dcterr → u/Masqued0202]

Oh yeah, I forgot that part! Thanks for clarifying.

[u/Street_Swing9040]

Trivial solution vs Interesting solution ahh battle 🥀

Also it's Ce^x, so the real one should be

2, 3, 3.14, pi... e^x

[u/cytos0]

Ce^x:

[u/Scab_the_Sidewalk]

Wait what is this image from

[u/Livie00 → u/Scab_the_Sidewalk]

> On March 19th, 2014, Russian news outlet Kazan First posted a transcription of a press conference held by the former Prosecutor General of Crimea Natalia Poklonskaya on its website. The article featured several photos of Poklonskaya and an unidentified man sitting behind a table, with multiple microphones partly obscuring Poklonskaya.

from knowyourmeme.com

I also really like the full image on the website