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), the derivative is as follows:
Or, in words:
= the derivative of the outer function multiplied by the derivative of the inner function.
Thus, let's take a look at the question.
The outer function is tan and the inner function is 3x, since 3x is ""inside"" the tan. Think of it as tan(u) where , so the 3x is composed in the tan. Deriving, we get:
The derivative of the outer function (without considering the inside function):
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