Hi guys,

I've got this exercise where i've gotten stuck on. Diﬀerentiate $\displaystyle ln(cos(1/x )) $ on its domain of deﬁnedness. I'm hoping I can get some guidance/help if i've gone wrong in what i've already done and in completing it.

$\displaystyle d, dx ln(cos(1/

x ))$

I choose to use the chain rule as there is a composition of functions.

We take $\displaystyle 1/x$ to be the inner function and cos to be the outer function.

$\displaystyle d,dx cos = -sin $

$\displaystyle d,dx 1/ x = -1/x^2$

which leaves me with

$\displaystyle d, dx ln( -sin. -1/x^2)$

From here I don't how to conitue or if i even should

Please help!. I apologize for how the maths terms are displayed, I'm quite new to the site and don't know any of the commands to make fractions symbols or anything else for that matter. Can't seem to find a help page that shows the maths commands, hence d by dx been display as it is, as well as 1 over x squared.

Thanks in advanced for any help you give