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.