[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]
