# How can i differentiate this ?

1. May 4, 2005

### abia ubong

I wonder if this can be differentiated ,if it can then what is the derivative of
[x^x^x^x^x^x.....]^[(x^2)^(x^2)^(x^2).....]^[(x^3)^(x^3)^(x^3).....]^[(x^4)^(x^5)...]......................
thank you

2. May 4, 2005

### Data

what do all the dots mean? What order do you want the exponentiation in (it's not associative)?

3. May 4, 2005

### dextercioby

From left to right i guess.I assume it resembles power tower.

Daniel.

4. May 4, 2005

### saltydog

The power tower:

$$y(x)=x^{x^{x^. . .}}}$$

is defined for:

$$e^{-e}\leq x\leq e^{1/e}$$

Note that the upper limit for a power tower is about 1.44467. However above, you're using "2" and larger values, you know $x^2$ and more. Thus I claim the expression is 0 for x<1, 1 for x=1, and infinity for x>1. It's derivative therefore is zero for $0\leq x\leq 1$ and undefined for x>1.

However, I've just started looking at it and wouldn't bet more than a dollar.

5. May 9, 2005

### An Average Joe

Here's a better question - "Can you draw the graph of it ?"

If you cannot draw a graph of that thing, then chances are pretty good that you cant differentiate it either.