Question

Y=(6+3X)^2/3 Find the derivative of the function using the chain rule

Answer 1

`\bf y=(6+3x)^{(2)/(3)}\implies \cfrac{dy}{dx}=\stackrel{chain~rule}{\cfrac{2}{3}(6+3x)^{(2)/(3)-1}\cdot (0+3)} \\\\\\ \cfrac{dy}{dx}=\cfrac{2}{3}(6+3x)^{-(1)/(3)}\cdot 3\implies \cfrac{dy}{dx}=2(6+3x)^{-(1)/(3)}\implies \cfrac{dy}{dx}=\cfrac{2}{\sqrt[3]{6+3x}}`