What this is
Derivative Calculator differentiates an expression and writes out every rule it used, in the order it used them. The answer matters, but the sequence of rules is the part you have to reproduce in an exam or a problem set, so it is the part the page is built around.
How it is built
The symbolic engine is written from scratch in plain JavaScript: a tokenizer and recursive-descent parser, an exact rational arithmetic layer, a canonical simplifier, a LaTeX writer and the differentiator itself. Nothing is outsourced to a computer-algebra library, which is what makes it possible to record a named rule at every node.
Because the whole engine runs in your browser, there is no server to send an expression to. That keeps it fast, keeps it working offline once loaded, and means your input stays on your own device.
Where the answers are checked
Every symbolic result in the test suite is compared against a central finite difference at several sample points, and every worked example on the rule pages is differentiated by the engine and checked against the answer the page states. A rule page cannot ship with an example the engine disagrees with.
What it does not do
Implicit differentiation and antiderivatives are not implemented. The absolute value is differentiated as sgn(u)·u′, which is correct everywhere except where u is zero. Factor cancellation is deliberately conservative: where a reduction cannot be justified, the answer is left in its longer form rather than risking a wrong one.
Get in touch
Corrections and requests are welcome — the contact page goes straight to the maintainers, or write to hello@derivativescalculator.org.