How to use the tabs 01 Derivative: enter an expression, the variable and an order up to 6; each higher-order pass is its own step. 02 Integral: enter an expression in one variable; the constant of integration is added as a step and the result is differentiated back as a verification step. 03 Solve: enter an equation with =; degree-2 equations show three methods — factoring, completing the square and the quadratic formula — then substitute each root back. 04 Simplify / Arithmetic: expand and collect terms, or compute gcd, lcm and exact fraction arithmetic with a common-denominator step. 05 Matrix: paste rows separated by ; (max 8×8) and choose Gauss-Jordan, Determinant or Inverse; row operations appear as numbered steps. Worked readouts
Tab · input
Readout
Derivative x^2*sin(x)
result x^2cos(x) + 2 x*sin(x) ; 2 steps — Product rule (2 sub-steps), then Simplify
Derivative, order 2
result −x^2sin(x) + 4 xcos(x) + 2 sin(x) ; steps Derivative #1 , Derivative #2
Integral x*e^x
result e^x*x − e^x + C ; 3 steps — Integration by parts (4 sub-steps), constant, Check: differentiate back ✓
Integral 3x^2+2x+1
result x^3 + x^2 + x + C ; verified
Solve x^2-5x+6=0
result x = 2, x = 3 ; 5 steps — Δ = 1 , (x−2)(x−3) = 0, (x−5/2)² = 1/4 , quadratic formula, verification
Simplify (x+1)^2
result x^2 + 2*x + 1 ; steps Expand, Combine like terms
Matrix 2 1; 1 3 with rhs 5 10
x1 = 1, x2 = 3 ; 6 steps ending in Back-substitution
Determinant 4 7; 2 6
10 , one step: 4·6 − 7·2
Inverse 4 7; 2 6
3/5 −7/10; −1/5 2/5 ; 7 steps, verified A·A⁻¹ = I
Arithmetic 1/2+1/3
5/6 ; steps Common denominator LCD = 6 , then add numerators
The integral result checks itself: differentiating e^x·x − e^x returns the input, which is what the green ✓ row means. The Gauss-Jordan run reads as a textbook page — R1 ← R1/2, R2 ← R2 − 1·R1, R2 ← R2/(5/2), R1 ← R1 − 1/2·R2 — then reads the solution off the reduced matrix.
What "verified" means Two tabs verify mechanically. The integral tab differentiates its own answer back and only then marks the derivation verified; the equation tab substitutes every root into the original equation. The matrix inverse tab multiplies A by the result and shows the identity. When the rule library has no match — try ∫e^(x²)dx — the panel stops, shows no rule matched , keeps the result unverified , and offers the answer from a computer-algebra fallback without a step-by-step explanation. The verified badge is a claim about the shown work, so it stays off there.
Limits
Finite rule libraries. Derivatives and integrals are decomposed with a fixed rule set; an expression outside it returns an unverified CAS answer with no steps rather than a fabricated derivation.
Caps on order and size. Derivative order ≤ 6, matrices ≤ 8×8, equations must be solvable in one variable. Arithmetic works in exact fractions, not floating point. What it doesn't do. It does not prove identities, handle systems with parameters, or solve differential equations; for numeric root scans and companion-matrix roots use equations , for matrix algebra beyond row operations use matrix tools . Syntax that trips people up log(x) means the natural logarithm here, not the base-10 log — write log10(x) for that. Implicit multiplication works (2x, 3sin x), ^ is right-associative (2^3^2 is 2⁹), and the variable field must match the expression: differentiating x^2*sin(t) with variable x treats t as a constant. The support note under the input lists the accepted functions, and the example chips are the fastest way to see the intended syntax.
Where it is useful Homework and exam preparation The three-method quadratic derivation is a revision sheet on its own: discriminant, factoring, completing the square, formula, substitution. Change the coefficients and watch which method carries the step count.
Checking a hand calculation Enter the matrix inverse and read the row operations against your own working; the final identity step catches a sign slip immediately. The integral tab does the same for antiderivatives — a wrong sign usually fails the differentiate-back check.
Privacy Parsing, derivations and verification all run in your browser; nothing you enter is uploaded.
References
Wikipedia, Product rule , en.wikipedia.org （访问日期：2026-10-07）— (uv)′ = u′v + uv′.
Wikipedia, Integration by parts , en.wikipedia.org （访问日期：2026-10-07）— ∫u dv = uv − ∫v du.
Wikipedia, Gaussian elimination , en.wikipedia.org （访问日期：2026-10-07）— row operations and back-substitution.
Wikipedia, Quadratic formula , en.wikipedia.org （访问日期：2026-10-07）— discriminant and completing the square.
Wikipedia, Elementary function , en.wikipedia.org （访问日期：2026-10-07）— why some antiderivatives have no elementary form.
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Reviewed by CalcX Editorial Team
Updated 2026-10-07