Why is pic related true?

Take the derivative of the Taylor expansion brainlet

>>8865020
It was discovered when playing around with the limits of series that arise in finance.

Was Euler on the spectrum?

>>8865162
Everyone unironically doing anything beyond calculus I is on the spectrum.

>>8865048

derive the taylor expansion without the derivative first.

By calculating an intrest wrongly

It's not that hard.
>ancient brainlet trying to differentiate exponential function
[eqn]f'(x)=\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h} = a^x \lim_{h \rightarrow 0} \frac{a^h-1}{h}[/eqn]
which naturally begs the question how the limit
[eqn]\lim_{h \rightarrow 0} \frac{a^h-1}{h}[/eqn]
behaves.

It's really not that hard to guess nonrigorously that there's a number a such that the above limit is 1, and that the value of a is
[eqn]\lim_{t\rightarrow 0}(1 + t)^{1/t}[/eqn]
because thats like the perfect thing to cancel out the other shit, assuming nonrigorously that we can interchange the limits and all that shit.

I don't know.

>>8865154
https://youtu.be/AuA2EAgAegE?t=3m

>>8865020
Look at the definition of the exp() function. It is in terms of a series.
If you calculate the derivative of each you will get the same series again.