How and why are these two similar looking functions different? I have two functions 1) $y=x^{x^{x}}$ 2) $y=(x^x)^x$
These two functions seem same to me and I just see it as a mere difference of writing style but when I graph it using an online graph plotter they have different curves also when I find their derivatives using logarithmic differentiation I get different results.For 1 and 2 I got $dy/dx$ as $x^{x^{x}}[x^x\cdot\ln(x)[1+\ln(x)]+x^{(x-1)}]$ and $(x^x)^x[x[2\ln(x)+1]]$  respectively
So,my question is ,Are these two functions really different,if yes ,how?If no,how can you justify their similar looking expressions?

Note that the exponent of $y=x^{x^x}$ can be represented as $k=x^x$ so $y=x^k$. For $y=(x^x)^x$ the exponent inside of the bracket is multiplied with the outside exponent so $k=x\cdot x= x^2$ then $y=x^k=x^{x^2}$
