Derivative walkthrough
Differentiate an expression symbolically and see which rule was used at every step. Numerical spot checks compare the answer with central differences at five points.
Expressions are limited to 1,000 characters, 512 symbols, 24 nesting levels and 100 digits per number, with a fixed step budget. Supported functions are sin, cos, tan, asin, acos, atan, exp, ln, log, sqrt and abs. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report and a CSV of spot checks. Use x for the variable, ^ for powers and functions such as sin(x) or ln(x). Up to 1,000 characters. Review the settings before running.
Your result
How to use Derivative walkthrough
- Type the expression, such as x^3*ln(x).
- Choose the variable and add assumptions such as x > 0 if you want them used.
- Run the walkthrough and read the rules, the simplified derivative and any conditions.
- Check the spot checks, then download the JSON report or the CSV of checks.
Useful next steps
Rules and steps
The tool applies the constant, sum, product, quotient, power, exponential, logarithm, trigonometric and chain rules to each part of the expression and lists them from the outside in. Letters other than the chosen variable are treated as constants. Method: OpenStax, Calculus Volume 1, chapter 3 Derivatives (2016).
Simplifying safely
Rewrites that change where an expression is defined, such as x^3/x to x^2 or sqrt(x^2) to x, are only applied when your assumptions allow them, for example x > 0. Otherwise they are listed as gated rewrites and the safe form is kept. Conditions such as x > 0 for ln(x) or x != 0 for x^-1 are listed separately.
Spot checks are evidence, not proof
The derivative is evaluated at five fixed points and compared with a central difference of the original expression. Points where either value is undefined are marked undefined and are not compared. The report counts the compared points and says the checks agree only when at least one point was compared and none disagreed, so sqrt(x - 5), which is undefined at all five points, gets no claim of agreement.