# How do you find the derivative of #y=tan(3x)# ?

##### 1 Answer

Well, you could do this using the chain rule, since there is a function within a function (a "composite" function). The chain rule is:

If you have a composite function F(x), then the derivative is:

Or, in words:

=the derivative of the outer function with the inside function left alone **times** the derivative of the inner function.

So let's look at your question.

The outer function is tan and the inner function is

The derivative of the outer function (leaving the inside function alone):

The derivative of the inner function:

Combining, we get: