Derivative of 1/x^6
Answer
-6*x^(-7)
Derivative of 1/x^6
- Rule Used
- Quotient Rule
- Steps
- Identify a quotient in 1/: use the quotient rule (u/v)' = (u'v − uv')/v². The minus sign belongs to the derivative of the denominator; swapping it is the usual error.
- Differentiate numerator and denominator, then combine.
- Final answer: -
The derivative of 1/x^6 is -6*x^(-7).
Instant step-by-step solution for 1/x^6
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Derivative of 1/x^6 = -6*x^(-7) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-1-minus-over-minus-x-minus-to-minus-the-minus-6
How to find the derivative of 1/x^6
To find the derivative of 1/x^6, 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 1/x^6?▼
The derivative of 1/x^6 is -6*x^(-7).
How do you find the derivative of 1/x^6?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -6*x^(-7).
Why is the derivative of 1/x^6 equal to -6*x^(-7)?▼
Because differentiation measures how a function changes — applying the rules to 1/x^6 yields -6*x^(-7). See the full step-by-step breakdown above.