# Derivative of pentation

1. May 27, 2012

### Ramanujan

How do I find the derivative of the first pentation function, i.e. x pentated to x. i cant even notate this in my graphing program so i dont know how to ask it to derive this function. pentation is the 5th hyperoperation, coming after tetration which is after exponentiation etc. x tetrated to n is x^x^x n times. tetration can be written as x^x and thus grapher and wolfram alpha can derive this function. pentation on the other hand, is x tetrated n times, which can not be written as a function in terms of multiplication or exponentiation, and thus i have no way of telling graphing programs what it is as a function.

2. May 27, 2012

### algebrat

How about if you take the natural log of both sides approximately $n$ times?