Derivative of 1/sqrt(6-x^2)
Answer
(-x^2+6)^(-3/2)*x
Derivative of 1/sqrt(6-x^2)
- 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: (-+6)^(-3/2)*x
The derivative of 1/sqrt(6-x^2) is (-x^2+6)^(-3/2)*x.
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Derivative of 1/sqrt(6-x^2) = (-x^2+6)^(-3/2)*x Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-1-minus-over-minus-sqrt6-minus-x-minus-to-minus-the-minus-2
How to find the derivative of 1/sqrt(6-x^2)
To find the derivative of 1/sqrt(6-x^2), 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/sqrt(6-x^2)?▼
The derivative of 1/sqrt(6-x^2) is (-x^2+6)^(-3/2)*x.
How do you find the derivative of 1/sqrt(6-x^2)?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is (-x^2+6)^(-3/2)*x.
Why is the derivative of 1/sqrt(6-x^2) equal to (-x^2+6)^(-3/2)*x?▼
Because differentiation measures how a function changes — applying the rules to 1/sqrt(6-x^2) yields (-x^2+6)^(-3/2)*x. See the full step-by-step breakdown above.