Question

Find the derivative. y = 5/ (2root4(x^3))

Answer 1

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

$\bf \cfrac{dy}{dx}=-\cfrac{15}{8x^{\frac{7}{4}}}\implies \cfrac{dy}{dx}=-\cfrac{15}{8\sqrt[4]{x^7}}\\\\\\ \cfrac{dy}{dx}=-\cfrac{15}{8x\sqrt[4]{x^3}}$