Derivative of 1/(x^3+1)
Answer
-3*(1+x^3)^(-2)*x^2
Derivative of 1/(x^3+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: -3*(1+)^(-2)*
The derivative of 1/(x^3+1) is -3*(1+x^3)^(-2)*x^2.
Instant step-by-step solution for 1/(x^3+1)
Share this result
Derivative of 1/(x^3+1) = -3*(1+x^3)^(-2)*x^2 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-1-minus-over-minus-x-minus-to-minus-the-minus-3-minus-plus-minus-1
How to find the derivative of 1/(x^3+1)
To find the derivative of 1/(x^3+1), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of x^(1/3)
Solve d/dx x^(1/3)
Derivative of x^(1/2)
Solve d/dx x^(1/2)
Derivative of 1-x
Solve d/dx 1-x
Derivative of 10^x
Solve d/dx 10^x
Derivative of 2^x
Solve d/dx 2^x
Derivative of 2x
Solve d/dx 2x
Derivative of 3x^2
Solve d/dx 3x^2
Derivative of 5x
Solve d/dx 5x
Derivative of Abs(x)
Solve d/dx Abs(x)
Derivative of acos(x)
Solve d/dx acos(x)
Frequently Asked Questions
What is the derivative of 1/(x^3+1)?▼
The derivative of 1/(x^3+1) is -3*(1+x^3)^(-2)*x^2.
How do you find the derivative of 1/(x^3+1)?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -3*(1+x^3)^(-2)*x^2.
Why is the derivative of 1/(x^3+1) equal to -3*(1+x^3)^(-2)*x^2?▼
Because differentiation measures how a function changes — applying the rules to 1/(x^3+1) yields -3*(1+x^3)^(-2)*x^2. See the full step-by-step breakdown above.