[tex]\bf y=\cfrac{5}{2\sqrt[4]{x^3}}\implies y=\cfrac{5}{2}\cdot x^{-\frac{3}{4}}\\\\
-----------------------------\\\\
\cfrac{dy}{dx}=\cfrac{5}{2}\left( -\cfrac{3}{4}x^{-\frac{3}{4}-1} \right)\implies
\cfrac{dy}{dx}=\cfrac{5}{2}\left( -\cfrac{3}{4}x^{-\frac{7}{4}} \right)
\\\\\\
\cfrac{dy}{dx}=-\cfrac{15}{8}\cdot x^{-\frac{7}{4}}
\implies
\cfrac{dy}{dx}=-\cfrac{15}{8}\cdot \cfrac{1}{x^{\frac{7}{4}} }
\\\\\\
[/tex]
[tex]\bf
\cfrac{dy}{dx}=-\cfrac{15}{8x^{\frac{7}{4}}}\implies
\cfrac{dy}{dx}=-\cfrac{15}{8\sqrt[4]{x^7}}\\\\\\ \cfrac{dy}{dx}=-\cfrac{15}{8x\sqrt[4]{x^3}}
[/tex]
