Question

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

Answer 1

`(2x)/(x^4 + 2x^2 + 2 )`

Explanation:

Using the `color(blue)" chain rule "`

`d/dx [ f(g(x)) ] = f'(g(x)) . g'(x)`

and the standard derivative `d/dx(tan^-1 x) = 1/(1 + x^2)`

`rArr d/dx(tan^-1(x^2+1)) = 1/(1+(x^2+1)^2) . d/dx(x^2+1)`

`= (2x)/(1+x^4+2x^2+1) = (2x)/(x^4+2x^2+2)`