Derivative Of A Stacked Exponential

It can be clearly seen that at x = 1, f(x) = 1.

I will be using y instead of f(x) and y' instead of f'(x)

$y = \frac{1}{x}^{x^{y}}$ $lny = -x^y lnx$ $-lny = e^{y lnx} lnx$

Differentiating...

$-\frac{1}{y} y' = (...)lnx + e^{y lnx} \frac{1}{x}$ Put x=1 and y=1 $-y' = 0 + 1$ $y' = -1$ $\boxed{|y'| = 1}$