Comment on Naturally

Illecors@lemmy.cafe ⁨1⁩ ⁨day⁩ ago

• ChaoticNeutralCzech@feddit.org ⁨1⁩ ⁨day⁩ 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.

  source

  • felsiq@piefed.zip ⁨1⁩ ⁨day⁩ 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

    source

    • knomie@feddit.org ⁨22⁩ ⁨hours⁩ 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.

      source

      • felsiq@piefed.zip ⁨14⁩ ⁨hours⁩ ago

        I wish I could say I commented this late at night or something, but nope I’m just dumb lmao thanks

        source
  • Illecors@lemmy.cafe ⁨1⁩ ⁨day⁩ ago

    Much appreciated!

    source
  • cRazi_man@europe.pub ⁨1⁩ ⁨day⁩ ago

    i.kym-cdn.com/photos/images/original/…/a12.jpg

    source
• arschflugkoerper@feddit.org ⁨1⁩ ⁨day⁩ ago

  The derivative of e^x is e^x

  source
• ManeraKai@programming.dev ⁨1⁩ ⁨day⁩ ago

  The derivative of e^x is always e^x: www.youtube.com/watch?v=oBlHiX6vrQY

  source

  • teft@piefed.social ⁨1⁩ ⁨day⁩ ago

    If you want to use exponents on the fediverse you have to enclose the entire exponent in carats like so without the spaces:

    e ^ x ^

    e^x

    source
  • anothercatgirl@lemmy.blahaj.zone ⁨1⁩ ⁨day⁩ ago

    how about derivative with respect to time instead of with respect to x?

    source

    • ChaoticNeutralCzech@feddit.org ⁨1⁩ ⁨day⁩ ago

       𝑒^𝑥^ has been around since the 17^th^ century and it hasn’t changed since. Therefore, it’s a constant with respect to time and gets unceremoniously derived to 0.

      source

      • anothercatgirl@lemmy.blahaj.zone ⁨1⁩ ⁨day⁩ ago

        very nicely said, I agree

        source
      • NobodyElse@sh.itjust.works ⁨1⁩ ⁨day⁩ ago

        Well played!

        source