[tex]\it f'(x)=\Big(\dfrac{x}{x^2+1}\Big)'=\dfrac{x'(x^2+1)-x(x^2+1)'}{(x^2+1)^2}=\dfrac{x^2+1-x\cdot2x}{(x^2+1)^2} =\dfrac{1-x^2}{(x^2+1)^2}[/tex]
