Step 1 :Find the first derivative of the function \(y=\sqrt[3]{x}\). The derivative is \(y'=\frac{1}{3}x^{-\frac{2}{3}}\).
Step 2 :Find the second derivative by taking the derivative of the first derivative. The second derivative of the function \(y=\sqrt[3]{x}\) is \(y''=-\frac{2}{9}x^{-\frac{5}{3}}\).
Step 3 :Final Answer: The second derivative of the function \(y=\sqrt[3]{x}\) is \(\boxed{-\frac{2}{9}x^{-\frac{5}{3}}}\).