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^{-(3)/(4)}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=\cfrac{5}{2}\left( -\cfrac{3}{4}x^{-(3)/(4)-1} \right)\implies \cfrac{dy}{dx}=\cfrac{5}{2}\left( -\cfrac{3}{4}x^{-(7)/(4)} \right) \\\\\\ \cfrac{dy}{dx}=-\cfrac{15}{8}\cdot x^{-(7)/(4)} \implies \cfrac{dy}{dx}=-\cfrac{15}{8}\cdot \cfrac{1}{x^{(7)/(4)} } \\\\\\`


`\bf \cfrac{dy}{dx}=-\cfrac{15}{8x^{(7)/(4)}}\implies \cfrac{dy}{dx}=-\cfrac{15}{8\sqrt[4]{x^7}}\\\\\\ \cfrac{dy}{dx}=-\cfrac{15}{8x\sqrt[4]{x^3}}`