LaTeX Calculus Cheat Sheet | Complete Math Symbols Reference

🚀 Quick Start Guide

LaTeX math is written between dollar signs: $formula$ for inline math or $$formula$$ for displayed equations. Packages like amsmath provide additional functionality.

📈 Derivatives & Differentiation

Basic Derivatives

\frac{dy}{dx}

$\frac{dy}{dx}$

f'(x)

$f'(x)$

\frac{d}{dx}[f(x)]

$\frac{d}{dx}[f(x)]$

\dot{x}

$\dot{x}$

\ddot{x}

$\ddot{x}$

Higher Order Derivatives

\frac{d^2 y}{dx^2}

$\frac{d^2 y}{dx^2}$

f''(x)

$f''(x)$

\frac{d^n y}{dx^n}

$\frac{d^n y}{dx^n}$

f^{(n)}(x)

$f^{(n)}(x)$

\partial^2 f/\partial x^2

$\partial^2 f/\partial x^2$

Partial Derivatives

\frac{\partial f}{\partial x}

$\frac{\partial f}{\partial x}$

\frac{\partial^2 f}{\partial x \partial y}

$\frac{\partial^2 f}{\partial x \partial y}$

\nabla f

$\nabla f$

\nabla \cdot \mathbf{F}

$\nabla \cdot \mathbf{F}$

\nabla \times \mathbf{F}

$\nabla \times \mathbf{F}$

∫ Integrals & Summation

Basic Integrals

\int f(x) \, dx

$\int f(x) \, dx$

\int_{a}^{b} f(x) \, dx

$\int_{a}^{b} f(x) \, dx$

\iint f(x,y) \, dx\,dy

$\iint f(x,y) \, dx\,dy$

\iiint f(x,y,z) \, dV

$\iiint f(x,y,z) \, dV$

\oint_C f(z) \, dz

$\oint_C f(z) \, dz$

Summation & Products

\sum_{i=1}^{n} a_i

$\sum_{i=1}^{n} a_i$

\prod_{i=1}^{n} a_i

$\prod_{i=1}^{n} a_i$

\lim_{x \to \infty} f(x)

$\lim_{x \to \infty} f(x)$

\lim_{x \to a^{+}} f(x)

$\lim_{x \to a^{+}} f(x)$

\bigcup_{i=1}^{n} A_i

$\bigcup_{i=1}^{n} A_i$

Differential Elements

\, dx

$dx$ (with space)

\!\mathrm{d}x

$\mathrm{d}x$ (upright d)

\frac{\mathrm{d}y}{\mathrm{d}x}

$\frac{\mathrm{d}y}{\mathrm{d}x}$

\Delta x

$\Delta x$

\delta x

$\delta x$

αβγ Greek Letters

\alpha

\beta

\gamma

\Gamma

\delta

\Delta

\epsilon

\varepsilon

\zeta

\eta

\theta

\Theta

\lambda

\Lambda

\mu

\nu

\xi

\Xi

\pi

\Pi

\rho

\sigma

\Sigma

\tau

\phi

\Phi

\psi

\Psi

\omega

\Omega

𝑓(𝑥) Functions & Operators

Elementary Functions

\sin(x)

$\sin(x)$

\cos(x)

$\cos(x)$

\tan(x)

$\tan(x)$

\log(x)

$\log(x)$

\ln(x)

$\ln(x)$

\exp(x)

$\exp(x)$

Advanced Functions

\sqrt{x}

$\sqrt{x}$

\sqrt[n]{x}

$\sqrt[n]{x}$

|x|

$|x|$

\lVert x \rVert

$\lVert x \rVert$

\langle x, y \rangle

$\langle x, y \rangle$

\binom{n}{k}

$\binom{n}{k}$

Operators

\pm

$\pm$

\mp

$\mp$

\times

$\times$

\cdot

$\cdot$

\div

$\div$

\circ

$\circ$

⟦⟧ Matrices & Vectors

Basic Matrix

\begin{pmatrix} a & b \\ c & d \end{pmatrix}

$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$

Bracket Matrix

\begin{bmatrix} a & b \\ c & d \end{bmatrix}

$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$

Determinant

\begin{vmatrix} a & b \\ c & d \end{vmatrix}

$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$

Vector

\begin{pmatrix} x \\ y \\ z \end{pmatrix}

$\begin{pmatrix} x \\ y \\ z \end{pmatrix}$

Inline Vector

\langle x, y, z \rangle

$\langle x, y, z \rangle$

System of Equations

\begin{cases} x + y = 1 \\ x - y = 0 \end{cases}

$\begin{cases} x + y = 1 \\ x - y = 0 \end{cases}$

∞ Special Symbols

Infinity & Limits

\infty

$\infty$

\lim_{x \to 0}

$\lim_{x \to 0}$

\to

$\to$

\rightarrow

$\rightarrow$

\Rightarrow

$\Rightarrow$

Sets & Logic

\in

$\in$

\subset

$\subset$

\subseteq

$\subseteq$

\cup

$\cup$

\cap

$\cap$

\emptyset

$\emptyset$

Calculus Symbols

\approx

$\approx$

\sim

$\sim$

\propto

$\propto$

\equiv

$\equiv$

\neq

$\neq$

\leq, \geq

$\leq, \geq$

💡 Pro LaTeX Tips

Use \, for small space, \; for medium space, \quad and \qquad for larger spaces
Always use \left( and \right) for automatic bracket sizing: \left( \frac{1}{2} \right)
For text within math mode, use \text{your text here}
Use \mathrm{d} for upright differential d in integrals: \int f(x) \mathrm{d}x
For multi-line equations, use align or gather environments
Include amsmath package for advanced math typesetting: \usepackage{amsmath}

📦 Essential LaTeX Packages

amsmath

Advanced math typesetting, align environments

amssymb

Additional mathematical symbols

geometry

Page layout and margins control

graphicx

Image inclusion and manipulation

hyperref

Hyperlinks within document

Bold math symbols: \bm{\alpha}

📝 Complete Example

\documentclass{article}
\usepackage{amsmath}
\begin{document}

The derivative of $f(x) = x^2$ is:
\[
f'(x) = \frac{d}{dx}[x^2] = 2x
\]

The definite integral from $a$ to $b$:
\[
\int_a^b f(x) \, dx = F(b) - F(a)
\]

Matrix multiplication:
\[
\begin{pmatrix}
a_{11} & a_{12} \\
a_{21} & a_{22}
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
=
\begin{pmatrix}
a_{11}x_1 + a_{12}x_2 \\
a_{21}x_1 + a_{22}x_2
\end{pmatrix}
\]

\end{document}