Consider the function f(x)=xxxf(x) = x^{x^x}f(x)=xxx for x>0x > 0x>0. Find the derivative f′(x)f'(x)f′(x) evaluated at x=1x = 1x=1.
f′(1)=0f'(1) = 0f′(1)=0
f′(1)=1f'(1) = 1f′(1)=1
f′(1)=ef'(1) = ef′(1)=e
f′(1)=1+ln(1)f'(1) = 1 + \ln(1)f′(1)=1+ln(1)