How do you differentiate arctan(x^2+1)?

2 Answers
Jun 22, 2016

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

Explanation:

let y = arctan (x^2 +1) so tan y = x^2 + 1

thus sec^2 y \ y' = 2x, \qquad y' = (2x)/(sec^2 y)

using identity tan^2 + 1 = sec^2 we have

y' = (2x)/(sec^2 y) = (2x)/((x^2 + 1)^2 + 1)

Jun 22, 2016

dy/dx=(2x)/(x^4+2x^2+2).

Explanation:

Let y=arctan(x^2+1)

Then, dy/dx=d/dx{arctan(x^2+1)} =1/{1+(x^2+1)^2}*d/dx(x^2+1)................[Chain rule]
=1/(1+x^4+2x^2+1)*2x=(2x)/(x^4+2x^2+2).