Question

What is the first derivative of 3\sqrt[3]{x^4}-12\sqrt[3]{x}?

Answer 1

$\bf y=3\sqrt[3]{x^4}-12\sqrt[3]{x}\implies y=3x^{\frac{4}{3}}-12x^{\frac{1}{3}} \\\\\\ \cfrac{dy}{dx}=3\left( \frac{4}{3}x^{\frac{1}{3}} \right)-12\left( \frac{1}{3}x^{-\frac{2}{3}} \right)\implies \cfrac{dy}{dx}=4x^{\frac{1}{3}}-4x^{-\frac{2}{3}} \\\\\\ \cfrac{dy}{dx}=4\sqrt[3]{x}-\cfrac{4}{\sqrt[3]{x^2}}$