yes it's fuckin me again i said why e to the x is its own derivative and the fuckin simplest explanation flew right over my head as i tried to make it more formal so i figured out i fuckin realised it's so fuckin trivial, everyone who says e^x is its own derivative because "muh that's what e is" is a reddit faggot who likes to dodge questions. why not assume that a person means "what does the idea of continuous interest (the limit for e) have to do with e being its own derivative"? exactly, they don't want to answer the fuckin question because they don't know guess what i got it right here. you know what, stop treating e as a number. e is a limit. stop asking "why is e^x its own derivative" , start asking "why do you get closer and closer to being your own derivative as a^x where a approaches e". alright let's take a look at the famous fuckin limit everyone knows this shit right lim(x->inf) (1 + 1/x)^x ok right now here's where the magic happens right, let x be some number right, let's raise it to the fuckin 1/x power ok so we get just 1 + 1/x and if you add 1/x to the power you fuckin multiply by 1 + 1/x and fuckin, adding 1/x is like adding to the x in the function and as that is like multiplying by 1+1/x you're fucking adding the current y value multiplied by the change in x which is 1/x so the idea is that if you have a number x in (1+1/x)^x (let's call this a), a^x will increase by itsself multiplied by 1/x for every 1/x, now if you fuckin get x to be as big as possible, bigger and bigger approaching e then you get a smaller and smaller increment which causes a change that is the y value multiplied by that increment so as the increment approaches 0 you get it being its own derivative so that's why e^x is its own derivative good luck reading this fuck you guys i wish i was just taught this fuckin