Derivative of 1/x^5
Answer
-5*x^(-6)
Derivative of 1/x^5
- 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^5 is -5*x^(-6).
Instant step-by-step solution for 1/x^5
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Derivative of 1/x^5 = -5*x^(-6) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-1-minus-over-minus-x-minus-to-minus-the-minus-5
How to find the derivative of 1/x^5
To find the derivative of 1/x^5, 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^5?▼
The derivative of 1/x^5 is -5*x^(-6).
How do you find the derivative of 1/x^5?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -5*x^(-6).
Why is the derivative of 1/x^5 equal to -5*x^(-6)?▼
Because differentiation measures how a function changes — applying the rules to 1/x^5 yields -5*x^(-6). See the full step-by-step breakdown above.