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^{(4)/(3)}-12x^{(1)/(3)} \\\\\\ \cfrac{dy}{dx}=3\left( (4)/(3)x^{(1)/(3)} \right)-12\left( (1)/(3)x^{-(2)/(3)} \right)\implies \cfrac{dy}{dx}=4x^{(1)/(3)}-4x^{-(2)/(3)} \\\\\\ \cfrac{dy}{dx}=4\sqrt[3]{x}-\cfrac{4}{\sqrt[3]{x^2}}`