# Power towers!

Calculus Level 5

Define $$\Large{ f }_{ n }=\underbrace{x^{ { x }^{ { . }^{ { . }^{ x } } } }}_{\text{n times}}$$.

Denote $$A=\displaystyle\lim _{ x\rightarrow 1 }{ \frac { { f }_{ n }(x)-{ f }_{ n-1 }(x) }{ (1-x)^{ n } } }$$, when $$n$$ is even.

And denote $$B=\displaystyle\lim _{ x\rightarrow 1 }{ \frac { { f }_{ n }(x)-{ f }_{ n-1 }(x) }{ (1-x)^{ n } } }$$, when $$n$$ is odd.

then find $$A-B$$

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