How do you differentiate y=ln( log(base 5) of x)?

Answer 1

That's a classic case of the Chain Rule: (f(g))' = f'(g) * g'

Obviously, ln'(g) = 1/g.

And remember that log-base-5(x) is just ln x/ln 5, so it's just a constant times something you already know how to differentiate.