# What is the derivative of #y=arctan(4x)#?

##### 1 Answer

**Answer**

**Explanation**

First recall that

Via the chain rule:

1.)

2.)

If it isn't clear why

We will begin simply with

1.)

From this it is implied that

2.)

Using implicit differentiation, taking care to use the chain rule on

3.)

Solving for

4.)

Which further simplifies to:

5.)

Next, a substitution using our initial equation will give us:

6.)

This might not look too helpful, but there is a trigonometric identity that can help us.

Recall

This simplifies to:

Now, simply multiply a few things around, and we get:

Beautiful. Now we can simply substitute into the equation we have in step 6:

7.)

And voilà - there's our identity.