Question

find y' of the functuion in terms of appropriate variable. simplify as far as possible.
y= ln(1+e^2x)^3

Answer 1

Can you confirm if it is

y=ln[(1+e^(2x))^3]

It never hurts to insert extra parentheses if you do not want unnecessary delay.

Answer 2

y = ln(1+e^2x)^3
= 3ln(ln(1+e^2x)

y' = 3(2e^(2x))/(1 + e^(2x))
= 6e^(2x) /(1 + e^(2x))