How can i differentiate this ?

[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

 

[Data]

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

 

[dextercioby]

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


Daniel.

 

[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.

 

[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 can't differentiate it either.