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

Answer

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Answer

Final Answer: The second derivative of the function $y=\sqrt[3]{x}$ is $\boxed{-\frac{2}{9}x^{-\frac{5}{3}}}$.

Steps

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

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

Answer

Popular Problems

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