Find the derivative.
\[
\frac{d}{d x}\left(\sqrt[3]{x}-\frac{4}{x}\right)
\]

Answer

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Answer

Final Answer: \(\boxed{\frac{1}{3}x^{-\frac{2}{3}} + \frac{4}{x^2}}\)

Steps

Step 1 ：Given the function \(f(x) = \sqrt[3]{x}-\frac{4}{x}\)

Step 2 ：We can rewrite the function as \(f(x) = x^{\frac{1}{3}} - 4x^{-1}\)

Step 3 ：Applying the power rule for derivatives, we get \(f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1} - 4(-1)x^{-1 - 1}\)

Step 4 ：Simplifying the expression, we get \(f'(x) = \frac{1}{3}x^{-\frac{2}{3}} + 4x^{-2}\)

Step 5 ：Finally, we can rewrite the derivative in a more standard form as \(f'(x) = \frac{1}{3}x^{-\frac{2}{3}} + \frac{4}{x^2}\)

Step 6 ：Final Answer: \(\boxed{\frac{1}{3}x^{-\frac{2}{3}} + \frac{4}{x^2}}\)