LaTeX
\frac{d}{dx}\ln x=\frac{1}{x}Variables
- x: positive real variable
How to use this formula
Differentiates the natural logarithm on its real domain.
Important notes
- For ln|x| the same derivative holds where x≠0.
Quick example
d ln(2x)/dx=1/x.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For ln|x| the same derivative holds where x≠0.
- For the Derivative of Natural Logarithm, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- Logarithm arguments must be positive in the real domain, and the base must be stated when it is not implied.
- The function must satisfy the differentiability, continuity, or integrability conditions required by the operation being used.
Worked example
d ln(2x)/dx=1/x.
Common mistakes
- When copying Derivative of Natural Logarithm, 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 of Natural Logarithm 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}\ln x=\frac{1}{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 of Natural Logarithm used for?
Differentiates the natural logarithm on its real domain.
Can I copy this formula as LaTeX?
Yes. Copy \frac{d}{dx}\ln x=\frac{1}{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.