Derivative of x^(1/3)
Answer
(1/3)*x^(-2/3)
Derivative of x^(1/3)
- Rule Used
- Power Rule
- Steps
- Identify the expression as a power function and apply the power rule. A rational exponent is allowed: ^(p/q) = (p/q)·.
- Final answer: (1/3)*
The derivative of x^(1/3) is (1/3)*x^(-2/3).
Instant step-by-step solution for x^(1/3)
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Derivative of x^(1/3) = (1/3)*x^(-2/3) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-1-minus-over-minus-3
How to find the derivative of x^(1/3)
To find the derivative of x^(1/3), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
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Frequently Asked Questions
What is the derivative of x^(1/3)?▼
The derivative of x^(1/3) is (1/3)*x^(-2/3).
How do you find the derivative of x^(1/3)?▼
Apply the standard differentiation rules — the key rule used here is the Power Rule. The step-by-step result is (1/3)*x^(-2/3).
Why is the derivative of x^(1/3) equal to (1/3)*x^(-2/3)?▼
Because differentiation measures how a function changes — applying the rules to x^(1/3) yields (1/3)*x^(-2/3). See the full step-by-step breakdown above.