Could someone show me how to get the derivative of both sides of this equation? I can't quite seem to figure it out. I have an answer, but I'm not sure it is not correct. Thanks for looking.

Here is what I have so far:

y= ln x, so x= e^y

which gives 1= e^y dy/dx

then 1/e^y= dy/dx

which gives 1/e^lnx=dy/dx

and lastly dy/dx= 1/x

Good or not so good?