## Calculus: Early Transcendentals 8th Edition

$f'(x) = \frac{1}{x~\cdot~ln~x~\cdot ~ln~ln~x}$ The domain is $~~(e, \infty)$
$f(x) = ln~ln~ln~x$ We can differentiate $f(x)$: $f'(x) = \frac{1}{ln~ln~x}\cdot \frac{d}{dx}(ln~ln~x)$ $f'(x) = \frac{1}{ln~ln~x}\cdot \frac{1}{ln~x} \cdot\frac{d}{dx}(ln~x)$ $f'(x) = \frac{1}{ln~ln~x}\cdot \frac{1}{ln~x} \cdot\frac{1}{x}$ $f'(x) = \frac{1}{x~\cdot~ln~x~\cdot ~ln~ln~x}$ When we consider the function $~~ln~ln~ln~x~~$ it is required that $~~ln~ln~x \gt 0$ Then $~~ln~x \gt 1$ Then $~~x \gt e$ The domain is $~~(e, \infty)$