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

1 Answer
Jul 12, 2016

(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.