Why does applying a natural log to both sides of an equal sign in order to find the derivative of a function (eg y=x^x) via implicit differentiation work?
[math]f^{(n)} (x)[/math] denotes the [math]n[/math]-th derivative of a function [math]f[/math]. Natural numbers for [math]n[/math] describe the successive rates of change of that function. However, what do fractional and irrational derivatives signify?