Re:The exponential function is a miracle
by dreamcompiler on Monday September 16, 2019 @11:04AM
(#20984774)
> Why is the base e? Why isn't it 2, like this
One of the many things that makes e special is that e^x is the only function that is its own derivative. One of the things that make sin and cos special is that they are each other's derivatives (except for a change of sign in the case of dcos/dx). This doesn't prove anything on its own, but it suggests that there might be some relationship between e and the trig functions, and Euler's equation proves that indeed there is.
One of the many things that makes e special is that e^x is the only function that is its own derivative. One of the things that make sin and cos special is that they are each other's derivatives (except for a change of sign in the case of dcos/dx). This doesn't prove anything on its own, but it suggests that there might be some relationship between e and the trig functions, and Euler's equation proves that indeed there is.