I'm trying to find the derivative of ln 2x

1) My textbook states that if y= ln [f(x)], then dy/dx= f '(x)/f(x)
2) According to a law of logs, ln 2x would be the same as ln2 + lnx


Here's my problem: Using method 1) the answer would be 2/2x
However using method 2), ln2 is a constant and so it can't be differentiated so the answer is 1/x

Which method is correct and where am i going wrong??