Derivative of 1/(x^2+6)^2
Answer
-4*(6+x^2)^(-3)*x
Derivative of 1/(x^2+6)^2
- Rule Used
- Quotient Rule
- Steps
- Identify a quotient in 1/(+6)^2: 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: -4*(6+)^(-3)*x
The derivative of 1/(x^2+6)^2 is -4*(6+x^2)^(-3)*x.
Instant step-by-step solution for 1/(x^2+6)^2
Share this result
Derivative of 1/(x^2+6)^2 = -4*(6+x^2)^(-3)*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-6-minus-to-minus-the-minus-2
How to find the derivative of 1/(x^2+6)^2
To find the derivative of 1/(x^2+6)^2, we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of asin(x)
Solve d/dx asin(x)
Derivative of atan(x)
Solve d/dx atan(x)
Derivative of cos(2x)
Solve d/dx cos(2x)
Derivative of cos(x)^2
Solve d/dx cos(x)^2
Derivative of cos(x)
Solve d/dx cos(x)
Derivative of cosh(x)
Solve d/dx cosh(x)
Derivative of cot(x)
Solve d/dx cot(x)
Derivative of csc(x)
Solve d/dx csc(x)
Derivative of e^(2x)
Solve d/dx e^(2x)
Derivative of e^(-x)
Solve d/dx e^(-x)
Frequently Asked Questions
What is the derivative of 1/(x^2+6)^2?▼
The derivative of 1/(x^2+6)^2 is -4*(6+x^2)^(-3)*x.
How do you find the derivative of 1/(x^2+6)^2?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -4*(6+x^2)^(-3)*x.
Why is the derivative of 1/(x^2+6)^2 equal to -4*(6+x^2)^(-3)*x?▼
Because differentiation measures how a function changes — applying the rules to 1/(x^2+6)^2 yields -4*(6+x^2)^(-3)*x. See the full step-by-step breakdown above.