Question

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

Answer 1

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