What is the derivative of ##ln e^(2x)##?

##y=ln(u)##

##:. dy/(du)=1/u=1/(e^(2x))##

##u=e^(2x)##, ##:. (du)/(dx)=2e^(2x)##

Now, using the ...

##(dy)/(du)*(du)/(dx)=1/(e^(2x))*2e^(2x)=2##

##:. (dy)/(dx)=2##

This all worked because:

When ##y=e^(f(x))##

##(dy)/(dx)=f'(x)e^(f(x))##