Partial Derivative in LaTeX (\partial)

Where it is used

Writes the curly ∂ for partial derivatives, and also boundaries of sets in topology.

\partial appears in partial derivatives such as \frac{\partial f}{\partial x} and mixed partials \frac{\partial^2 f}{\partial x\,\partial y}. In topology and geometry, \partial A is the boundary of a set or manifold, used in Stokes' theorem \int_{\partial M} \omega = \int_M d\omega. For short subscripted forms, \partial_x f and \partial_t u are common in PDE papers. Do not mix it up with \delta (variation) or d (total derivative). Placing a thin space between \partial factors in the denominator improves spacing.

Also listed under: Calculus & Analysis, Topology & Abstract Math

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Partial Derivative: $\partial$

\[ \frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2} \]
\end{document}

Related symbols

• Nabla\nabla
• Empty Set\emptyset
• Plus Minus\pm
• Intersection\cap
• Dot Product\cdot
• Union\cup

Frequently asked questions

How do I write Partial Derivative in LaTeX?

Type \partial in math mode, for example $\frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2}$. It works in plain LaTeX without loading any package.

Which package do I need for \partial?

None. \partial is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \partial in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\partial$ in running text. If you only need the glyph in text, paste the Unicode character ∂ instead (with XeLaTeX or LuaLaTeX and a font that has it).