Question

OK, here is a differentiation problem that is baffling me -- y = {ln[ln(ln x)]} -- What is y prime? I am guessing the chain rule is the key here, but I cannot figure out the solution.

Answer 1

[ln(ln x)] = z and ln x = t => z = ln t
y = ln z
y(prime) = z(prime)/z
z(prime) = t(prime)/t
t(prime) = 1/x
y(prime) = 1/xtz
y(prime) = 1/x*ln x*ln(ln x)