To start with, ln(5) is a constant. The derivative of a constant is 0. Fix that error and you should start to see things cancelling.
this question is the limit as t tends to infinity of T(ln(5+1/t) - ln(5))
I think im having an algebraic problem. basicly the problem can be arranged :
infinity times 0 =
(ln(5+1/t) - ln(5)) / 1/T
that makes it 0/0 so I can use L'hopitals.
so I take the derivatives and get this :
((1/(5+1/T))(-1/t^2) - 1/5) / (-1/t^2)
But im not sure what to do from here. Ive been trying different thigns but keep getting different answers. the right answers supposed to be 1/5. can someone break it down for me?