Derivative of 5/x
Answer
-5*x^(-2)
Derivative of 5/x
- Rule Used
- Quotient Rule
- Steps
- Identify a quotient in 5/x: 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 5/x is -5*x^(-2).
Instant step-by-step solution for 5/x
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Derivative of 5/x = -5*x^(-2) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-5-minus-over-minus-x
How to find the derivative of 5/x
To find the derivative of 5/x, 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 5/x?▼
The derivative of 5/x is -5*x^(-2).
How do you find the derivative of 5/x?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -5*x^(-2).
Why is the derivative of 5/x equal to -5*x^(-2)?▼
Because differentiation measures how a function changes — applying the rules to 5/x yields -5*x^(-2). See the full step-by-step breakdown above.