We use the log law:

log ab = log a + log b

We can write our question as:

y = ln 2x = ln 2 + ln x

Now, the derivative of a constant is 0, so

So we are left with

(from our formula above)

The final answer is:

We can see from the following graph that the slope of y = ln 2x (curve in black, tangent in red) is the same as the slope of y = ln x (curve in blue, tangent in pink), at the point x = 2.