LaTeX
\left(\frac{f}{g}\right)\prime=\frac{f\prime g-fg\prime}{g^2}Variables
- f,g: differentiable functions
- g: nonzero denominator
How to use this formula
Differentiates a quotient of two functions.
Important notes
- Keep the term order to preserve the sign.
Quick example
Differentiate x/(x+1) to get 1/(x+1)².
Applicability, worked calculation, and verification
Assumptions and domain checks
- Keep the term order to preserve the sign.
- For the Quotient Rule, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- The function must satisfy the differentiability, continuity, or integrability conditions required by the operation being used.
Worked example
Differentiate x/(x+1) to get 1/(x+1)².
Common mistakes
- When copying Quotient Rule, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Do not apply a differentiation or integration rule outside its domain or omit endpoint, continuity, or constant-of-integration checks.
Continue the workflow
Use Quotient Rule in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\left(\frac{f}{g}\right)\prime=\frac{f\prime g-fg\prime}{g^2}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Calculus Volume 1OpenStax, Rice University — Reviewed limits, derivatives, integrals, and foundational calculus formulas.
Frequently asked questions
What is the Quotient Rule used for?
Differentiates a quotient of two functions.
Can I copy this formula as LaTeX?
Yes. Copy \left(\frac{f}{g}\right)\prime=\frac{f\prime g-fg\prime}{g^2} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.