Respuesta :

[tex]\bf y=\cfrac{3x}{\sqrt{4x^2+1}}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=\cfrac{3\sqrt{4x^2+1}-3x\left[ \frac{1}{2}(4x^2+1)^{-\frac{1}{2}}\cdot 8x \right]}{(\sqrt{4x^2+1})^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{3\sqrt{4x^2+1}-\left[ \frac{24x^2}{2\sqrt{4x^2+1}} \right]}{(\sqrt{4x^2+1})^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{\frac{(3\sqrt{4x^2+1})(2\sqrt{4x^2+1})-24x^2}{2\sqrt{4x^2+1}}}{(\sqrt{4x^2+1})^2} \\\\\\[/tex]

[tex]\bf \cfrac{dy}{dx}=\cfrac{6(4x^2+1)-24x^2}{2\sqrt{4x^2+1}}\cdot \cfrac{1}{(\sqrt{4x^2+1})^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{24x^2+6-24x^2}{2\sqrt{4x^2+1}}\cdot \cfrac{1}{(\sqrt{4x^2+1})^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{6}{2\sqrt{(4x^2+1)^3}}[/tex]

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