Euler's number (e) was discovered as the real number that, if differentiated, would result in the original exponential function. You can differentiate e to the power of x multiple times and the resulting derivative(s) would remain as e to the power of x. This essentially means that the gradient of the curve is equivalent to f(x) for any given value of x
Why do we use e?
The number e (approximately 2.718) is special as the number has a unique property where the function y=e^x will have a gradient (or slope) of e^x for any real value of x over the entire function. This property allows us to differentiate and integrate exponential functions involving e to the power of a function.