Question

What is the derivative of `arctan(x^2+1)`?

Answer 1

`(2x)/((x^2+1)^2+1)`

Explanation:

Here we're going to use "u substitution."

Analyzing the problem `arctan(x^2+1)` we should probably use `x^2+1` as our `u`.

`arctan(u) | u = x^2+1`

The derivative of `arctan(u)` is `(du)/(u^2+1)`

The derivative of `u` is `du`, and so `du` is `2x` using the power rule. So now that we have our components, we just plug into the derivative of `arctan(u)` with our `u` and `du`.

`(2x)/((x^2+1)^2+1)` turns out to be our final answer after plugging our `u` and `du` values.