Answer
${dy}=(\frac{2-2x^2)}{(1+x^2)^2}){dx}$
Work Step by Step
We evaluate the function: $y=\frac{2x}{{(1+x^2)}}$
on differentiating the above:
$\frac{dy}{dx}=\frac{d\frac{2x}{(1+x^2)}}{dx}$
or ${dy}=(\frac{2(1+x^2)-2x\times2x}{(1+x^2)^2}){dx}$
or ${dy}=(\frac{(2+2x^2)-4x^2}{(1+x^2)^2}){dx}$
or ${dy}=(\frac{2-2x^2)}{(1+x^2)^2}){dx}$
The final answer is: ${dy}=(\frac{2-2x^2)}{(1+x^2)^2}){dx}$
