[tex]\bf y=\cfrac{7x}{3+x^2}\implies \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{7(3+x^2)-7x(0+2x)}{(3+x^2)^2}}
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\cfrac{dy}{dx}=\cfrac{21+7x^2-14x^2}{(3+x^2)^2}\implies \cfrac{dy}{dx}=\cfrac{21-7x^2}{(3+x^2)^2}\implies \cfrac{dy}{dx}=\cfrac{7(3-x^2)}{(3+x^2)^2}[/tex]
