Differentiate arctan of x with respect to x.

Say arctan of x is equal to a value y. Now take the tangent of both sides; x now equals tan of y! Easy from here, differentiate both sides wrt x. Now 1 equals sec^2y dy/dx, and you can rearrange to find dy/dx. To simplify, use the trig identity tan^y+1=sec^y, to get 1/1+x^2 is dy/dx.