Using the nth term test for ln(1/n) of divergence with n=1 and approaching infinity help

I know by the harmonic and p-series that it is divergent.
But I am asked to solve this test through the nth term.
After finding the derivative of the the problem. I got -1/n.
Wouldn't that be approaching zero?
I am a little rusty with my natural logs and can someone correct me please?
Thanks!

You can't take a derivative here. If the sum is

∞
Σ ln(1/n)
n=1

you can show that it is divergent by showing that lim(n->∞) ln(1/n) is not zero. It is in fact -∞. A simple way to conclude this is use the property of logs

ln(1/n) = ln(1) - ln(n) = 0 - ln(n).

Note also that ln(n) ->∞ as n -> ∞. So

lim ln(1/n) = -∞.
n->∞

Since the limit is not zero, the series diverges by the nth term test.

(Remember what the nth term test says. For Σ a_n, if the limit as n->∞ a_n is not zero, the series is divergent. If the limit turns out to be zero, then the test fails. That is, the series may or may not converge, so other testing is needed.)