# How can i differentiate this ?

• abia ubong
In summary, the conversation discusses the power tower function y(x)=x^{x^{x...}} and its derivative for different values of x. The upper limit for a power tower is approximately 1.44467, and the conversation also mentions using larger values such as x^2 and above. It is concluded that the function is 0 for x<1, 1 for x=1, and infinity for x>1, with a derivative of 0 for 0≤x≤1 and undefined for x>1. The possibility of graphing the function is also brought up as a potential challenge.
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

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

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

Daniel.

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.

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.

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