How to enter expressions.
Familiar algebraic syntax — use parentheses to be safe.
Operators
| Symbol | Meaning | Example |
|---|---|---|
| + − | Add, subtract | x^2 + 1, 3x − 2 |
| * / | Multiply, divide | 2*x, x/3, 1/(x+1) |
| ^ | Power (right-assoc.) | x^2, e^x, x^(n+1) |
| ( ) | Grouping | (x+1)*(x-1) |
| , | Function separator (reserved) | — |
Functions
All functions take a single argument in parentheses. Multi-character names are case-insensitive.
Constants and variables
- pi — the constant π (3.14159…).
- e — kept symbolic; use e^x for exp(x).
- Variables: pick from x, y, t, z in the dropdown.
Precedence
From highest to lowest: ^ → unary − → *, / → +, −. Use parentheses to override.
Common pitfalls
- Multiplication must be explicit between numbers and numbers, but implicit between numbers and variables: 2x ✓, xy ✓, 2 3 ✗.
- ln vs log. ln(x) is the natural log; log10(x) is base 10; log2(x) is base 2; log(x) is an alias for ln.
- Domain errors at evaluation. sqrt(-1), ln(0), 1/0 are surfaced as friendly messages rather than NaN.
How it works under the hood
When you enter an expression and press differentiate, the calculator processes it through a symbolic computation pipeline:
Tokenization (Lexer)
The input text is split into a stream of recognized symbols or "tokens" (e.g. operators like +, numbers like 3.14, variables like x, and functions like sin).
Parsing & Structural Analysis
A parser analyzer processes these tokens and transforms them into a form that is better understandable by a computer, namely a tree structure (an Abstract Syntax Tree, or AST). For example, 3*x + 1 becomes an addition root node, with a multiplication node on the left side and the number 1 on the right.
Symbolic Differentiation
The differentiator traverses the AST recursively, applying calculus rules (such as the sum, product, quotient, and chain rules) node by node to produce a raw derivative tree.
Algebraic Simplification
The raw derivative tree is simplified through multiple passes (constant folding, combining like terms, division reductions, and trigonometric identity rewrites) to generate a clean, readable result.