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