Type the expression with an equation editor, as on paper, choose what you want to do and get the exact answer —with fractions and roots, not decimals— and every step explained: the rule of each derivative, the factoring case, the discriminant of a quadratic or the Gauss-Jordan row operations.
A symbolic calculator works with expressions, not just numbers: it keeps √2 as √2 and 1/3 as 1/3 instead of rounding them, and it can differentiate, integrate or factor the way you do on paper. That matters in a math or engineering course, where the exact answer and, above all, the work are what count. This guide explains how to type expressions, what each part of the calculator does and works several typical exercises.
The field is an equation editor: what you type looks like a textbook. On the keyboard: / makes a fraction, ^ an exponent, sqrt a root and pi is π; Enter computes. Decimals are treated as exact fractions (0.5 = 1/2). The virtual keyboard, from the icon at the right of the field, has a tab with derivatives, integrals, limits, ∞, y′ and y″.
In the Compute tab the calculator decides what to do from the shape of what you type: without "=" it simplifies, with "=" it solves the equation, with <, >, ≤ or ≥ it solves the inequality, and it understands derivatives (d/dx), integrals, limits and differential equations with y′ and y″. Below the answer it offers other operations on the same expression. The other tabs (Algebra, Calculus, Series and differential equations, Several variables and Matrices) group the operations by topic so you can pick a specific one, and the "List of commands" shows how to ask for each.
1. Quadratic equation. x² − 5x + 6 = 0. The discriminant is Δ = b² − 4ac = 25 − 24 = 1 > 0, so there are two real roots:
x = (5 ± √1) / 2 ⟹ x = 2 or x = 3
This is the same as factoring: x² − 5x + 6 = (x − 2)(x − 3).
2. Derivative with the product rule. For f(x) = x²·sin x, with u = x² and v = sin x, (uv)′ = u′v + uv′:
f′(x) = 2x·sin x + x²·cos x
3. Chain rule. For sin(3x²), the outer function is sin and the inner one 3x², whose derivative is 6x:
d/dx [sin(3x²)] = cos(3x²) · 6x
4. Integral by substitution. In ∫ 2x·cos(x²) dx take u = x², so du = 2x dx and the integral becomes ∫ cos u du:
∫ 2x·cos(x²) dx = sin(x²) + C
Check: differentiating sin(x²) + C gives cos(x²)·2x, the original integrand.
5. Limit. limx→0 sin x / x has the form 0/0. By L'Hôpital's rule, differentiate the numerator and the denominator: limx→0 cos x / 1 = 1.
6. Linear system. x + y = 5 and x − y = 1. Adding the equations, 2x = 6, so x = 3 and y = 2. The calculator solves systems of any size and lets you pick the method (Gauss-Jordan, Cramer, inverse matrix, substitution…).
Before showing an indefinite integral, the calculator differentiates the antiderivative and checks that it gives the integrand back; solutions of equations and differential equations are substituted into the original equation. If it cannot verify a result, it does not present it as exact. Still, go over the steps: they are the part that helps you learn and pass the exam.
The topics in this guide are those of a calculus and linear algebra course, for example J. Stewart, Single Variable Calculus (Cengage), and G. Strang, Introduction to Linear Algebra. Simuveliq is not affiliated with these authors or publishers.
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