I had a student ask this the other day and I could find no immediate way to solve it without doing some serious work on it. Since then I've been mulling it over and came up with the following course of action to simplify the work. I'd like y'all to take a look at it and tell me if I've got it right.
Let y = 3x. Then the limit is
Now let H = 3h. Then the limit is
Then we do our magic with taking the derivative of the tangent function and get
Is this process of substitution acceptable in general? It works for this problem, but I'd like to verify that this can be generalized.