Derivative of 1/x^8
Answer
-8*x^(-9)
Derivative of 1/x^8
- 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^8 is -8*x^(-9).
Instant step-by-step solution for 1/x^8
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Derivative of 1/x^8 = -8*x^(-9) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-1-minus-over-minus-x-minus-to-minus-the-minus-8
How to find the derivative of 1/x^8
To find the derivative of 1/x^8, 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^8?▼
The derivative of 1/x^8 is -8*x^(-9).
How do you find the derivative of 1/x^8?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -8*x^(-9).
Why is the derivative of 1/x^8 equal to -8*x^(-9)?▼
Because differentiation measures how a function changes — applying the rules to 1/x^8 yields -8*x^(-9). See the full step-by-step breakdown above.