Derivative of a Complicated Power Equation

Calculus Level pending

Let \(f\left(x\right)=a^{\left(a^{x}\right)}\) and \(g\left(x\right)=log_{a} {x}\) where \(a\) is a constant.

What is the derivative of \(g\left(g\left(f\left(x\right)\right)\right)\)?

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