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