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(lemmy.world)
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this post was submitted on 08 Nov 2025
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Any explanation for the mathematically challenged?
She is derivation, a transform of functions that describes rate of π(π₯) changing as π₯ changes. (This can be represented visually as the slope of the graph π¦β=βπβ(π₯).) He is the exponential function π^π₯^, which is the only* non-zero function whose derivative is itself - in other words, unaffected by derivation. The number π is a constant (around 2.718) and the base of natural logarithms, hence the title.
* except its multiples such as β2βπ^π₯^, which are... just... uh... derivative works
Much appreciated!
https://i.kym-cdn.com/photos/images/original/000/913/758/a12.jpg
I think you forgot about e^x + 1, and e^x + 2, and β¦ β¦
(My profs always dunked on me for forgetting the + c and I canβt resist doing it to someone else, Iβm sorry)
For real tho, great explanation
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.
I wish I could say I commented this late at night or something, but nope Iβm just dumb lmao thanks
The derivative of e^x is e^x
The derivative of e^x is always e^x: https://www.youtube.com/watch?v=oBlHiX6vrQY
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^
how about derivative with respect to time instead of with respect to x?
βπ^π₯^ 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.
very nicely said, I agree
Well played!