Operation
Variable Order
Limits
to
Verbosity
Expression
Examples:
Examples:
Matrix A [[1,2],[3,4]] Tip: Use strings for symbols: [["a","b"],["c","d"]] Matrix B
[[5,6],[7,8]]
Examples:
Show JSON

## Result

Typeset Format
Output

### Step-by-Step Explanation

### Raw JSON

## Interactive Graph

### Supported Rules

📏 Basic Rules

- `diff_constant` — Constant → 0 e.g. 5, pi, e
- `diff_identity` — Identity → 1 e.g. x
- `sum_rule` — Sum: (f+g)' = f' + g' e.g. x + sin(x)
- `constant_multiple` — Constant multiple: (c·f)' = c·f' e.g. 3*x**2
- `power_rule` — Power: (x^n)' = n·x^(n-1) e.g. x**5
- `product_rule` — Product: (f·g)' = f'·g + f·g' e.g. x*sin(x)
- `quotient_rule` — Quotient: (f/g)' = (f'·g - f·g')/g² e.g. sin(x)/x
- `logarithmic_differentiation` — (u^v)' with both varying e.g. x**x

📐 Trigonometric

- `chain_rule_sin` — sin(u)' = cos(u)·u' e.g. sin(x**2)
- `chain_rule_cos` — cos(u)' = -sin(u)·u' e.g. cos(3*x)
- `chain_rule_tan` — tan(u)' = sec²(u)·u' e.g. tan(x**2)
- `chain_rule_sec` — sec(u)' = sec(u)tan(u)·u' e.g. sec(x)
- `chain_rule_csc` — csc(u)' = -csc(u)cot(u)·u' e.g. csc(x)
- `chain_rule_cot` — cot(u)' = -csc²(u)·u' e.g. cot(x)

🔄 Inverse Trig

- `chain_rule_asin` — asin(u)' = u'/√(1-u²) e.g. asin(x)
- `chain_rule_acos` — acos(u)' = -u'/√(1-u²) e.g. acos(x)
- `chain_rule_atan` — atan(u)' = u'/(1+u²) e.g. atan(x)
- `chain_rule_asec` — asec(u)' with chain rule e.g. asec(x)
- `chain_rule_acsc` — acsc(u)' with chain rule e.g. acsc(x)
- `chain_rule_acot` — acot(u)' with chain rule e.g. acot(x)

🌊 Hyperbolic

- `chain_rule_sinh` — sinh(u)' = cosh(u)·u' e.g. sinh(x**2)
- `chain_rule_cosh` — cosh(u)' = sinh(u)·u' e.g. cosh(x)
- `chain_rule_tanh` — tanh(u)' = sech²(u)·u' e.g. tanh(x)
- `chain_rule_asinh` — asinh(u)' with chain rule e.g. asinh(x)
- `chain_rule_acosh` — acosh(u)' with chain rule e.g. acosh(x)
- `chain_rule_atanh` — atanh(u)' with chain rule e.g. atanh(x)

📈 Exponential & Log

- `chain_rule_exp` — exp(u)' = exp(u)·u' e.g. exp(x**2)
- `chain_rule_log` — log(u)' = u'/u e.g. log(x)

🔬 Special Functions

- `chain_rule_erf` — erf(u)' = (2/√π)·exp(-u²)·u' e.g. erf(x**2)
- `chain_rule_gamma` — gamma(u)' = Γ(u)·ψ(u)·u' e.g. gamma(x)
- `chain_rule_heaviside` — Heaviside(u)' = δ(u)·u' e.g. Heaviside(x)
- `chain_rule_abs` — |u|' = sign(u)·u' e.g. Abs(x**3)
- `chain_rule_floor` — ⌊u⌋' = 0 (except at integers) e.g. floor(x)
- `chain_rule_ceiling` — ⌈u⌉' = 0 (except at integers) e.g. ceiling(x)

### Linear Algebra Operations

🔢 Matrix Operations

- `matrix_multiply` — Multiply two matrices element-by-element A × B
- `matrix_determinant` — Calculate determinant (2×2, 3×3, n×n) det(A)
- `matrix_inverse` — Find inverse matrix A⁻¹ A⁻¹ where AA⁻¹ = I
- `matrix_rref` — Row reduce to echelon form RREF(A)
- `matrix_eigenvalues` — Find eigenvalues and eigenvectors Av = λv
- `matrix_lu` — LU decomposition with pivoting PA = LU

💡 Symbolic Matrices: Use quoted strings for symbols: `[["a","b"],["c","d"]]`
Supports numeric, symbolic, and mixed entries!