I found that:
so I found the derivatives of them and I got:
I'm not sure on what I am doing wrong.
You haven't, technically, done anything wrong, except that, of course, because you cannot divide by 0, you cannot evaluate that final limit by simply setting . What you can do now is argue that, for x close to , but larger, sin(x) will be very close to 1 while cos(x) will be very close to 0 and negative. That gives the result that the limit is " " as MaxJasper said. I will add that " " is not a real number so that is just saying "the limit does not exist", in a particular way.