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According to given question

y=2x/x^2+1

By taking derivative

dy/dx=d/dy(2x/x^2+1)

y'=2(x^2+1)-2x(2x)/(x^2+1)^2

y'=2(x^2+1)-4x^2/(x^2+1)^2

y'=-2x^2+2/x^4+1+2X^2

At the origion

Y-y1=m(x-x1)

y-(-2x^2+2/_4x^2+1)

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