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submitted 6 days ago by themaninblack@lemmy.world to c/science_memes@mander.xyz

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[-] ChaoticNeutralCzech@feddit.org 45 points 6 days ago* (last edited 6 days ago)

She is derivation, a transform of functions that describes rate of 𝑓(𝑥) changing as 𝑥 changes. (This can be represented visually as the slope of the graph 𝑦 = 𝑓 (𝑥).) He is the exponential function 𝑒^𝑥^, which is the only* non-zero function whose derivative is itself - in other words, unaffected by derivation. The number 𝑒 is a constant (around 2.718) and the base of natural logarithms, hence the title.

* except its multiples such as −2 𝑒^𝑥^, which are... just... uh... derivative works

[-] Illecors@lemmy.cafe 6 points 6 days ago

Much appreciated!

[-] cRazi_man@europe.pub 3 points 6 days ago

https://i.kym-cdn.com/photos/images/original/000/913/758/a12.jpg

[-] felsiq@piefed.zip 1 points 6 days ago

the only* non-zero function whose derivative is itself

* except its multiples such as −2 𝑒𝑥, which are... just... uh... derivative works

I think you forgot about e^x + 1, and e^x + 2, and … …

(My profs always dunked on me for forgetting the + c and I can’t resist doing it to someone else, I’m sorry)

For real tho, great explanation

[-] knomie@feddit.org 6 points 6 days ago

But the derivative of e^x+c is just e^x (which for c!=0 is not the same). That's why the +c is added during integrating because all +c is derived to 0 and thus indistinguishable.