poprskanvxcl

## Answered question

2023-02-21

How to find the derivative of ?

### Answer & Explanation

affwysaumlgx

Beginner2023-02-22Added 12 answers

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):

The derivative of the inner function:

Combining, we get:

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?