Find the derivative $\frac{d}{dx}[arctan(x^2+1)].$

Select one:

$a.(arcsec(x^2+1){)}^2$

$b.\frac{1}{2+x^2}$

$c.\frac{1}{1+(x^2+1{)}^2}$

$d.\frac{2x}{1+(x^2+1{)}^2}$