Examining e^x, a curious function that is its own derivative.
What’s so special about e^x?
All right, so f’(x)=f(x), so what?
This is interesting. It appears as though exponential functions are the only ones of the form dR/dt=kR
That is to say, the growth at any given time is determined by the current value at a time. In the case of e^x, k would be equal to 1.
We should investigate other interesting cases; what about something that fits the form 2f’(x)=f(x)? And what of xf’(x)=f(x)? These are just simple differential equations that I don’t really have a great grasp on.