Find f(x)' of f(x)=x^x^x

Question

I logged both sides to get

ln y = x^x ln x

But I am not sure what step to do after that.

Answer 1

You are assuming y = f(x)

lny = x*(x^x)
(1/y)*dy/dx = x^x + x*(x^x)*(1 + lnx)
f'(x) = dy/dx
= f(x)*[x^x + x*(x^x)*(1 + lnx)]
= x^x^x*[x^x + x*(x^x)*(1 + lnx)]

I had to look up the derivative of x^x.