Problem

Find $\frac{d^{2} y}{d x^{2}}$ \[ y=\sqrt[3]{x} \] \[ \frac{d^{2} y}{d x^{2}}= \]

Solution

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 \(\boxed{-\frac{2}{9}x^{-\frac{5}{3}}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/12854/

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