LaTeX
\frac{d}{dx}f(g(x))=f\prime(g(x))g\prime(x)Variables
- Define every symbol and unit before substitution.
- Check the domain, shape, and convention required by the formula.
How to use this formula
Differentiates a composite function.
Important notes
- Verify assumptions and units before applying the expression.
- Keep exact values until the final rounding step when possible.
Quick example
Use the derivative chain rule with a small known example, then verify the result independently.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For the Derivative Chain Rule, verify assumptions and units before applying the expression.
- For the Derivative Chain 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
Use the derivative chain rule with a small known example, then verify the result independently.
Common mistakes
- When copying Derivative Chain 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 Derivative Chain 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
\frac{d}{dx}f(g(x))=f\prime(g(x))g\prime(x). - 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 Derivative Chain Rule used for?
Differentiates a composite function.
Can I copy this formula as LaTeX?
Yes. Copy \frac{d}{dx}f(g(x))=f\prime(g(x))g\prime(x) 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.