Partial derivative (∂) in LaTeX
\partial produces the partial-derivative symbol, used to differentiate a function of several variables with respect to one of them.
LaTeX command
\partialNot the symbol you meant? Draw it to find the command →
Partial derivatives are built with \frac, not with \partial alone: \frac{\partial f}{\partial x} reads as the partial of f with respect to x. The symbol is a mathematical object in its own right, so you assemble the derivative around it rather than treating it as a function.
For higher orders put the power on both \partial and the variable: \frac{\partial^2 f}{\partial x^2}. A mixed second partial adds a thin space between the variables, \frac{\partial^2 f}{\partial x\,\partial y}. Subscript shorthand such as f_x and f_{xy} is a compact alternative.
The same symbol denotes the boundary of a set or region in topology, written \partial \Omega, and the boundary operator. Context makes the meaning clear. Do not substitute the letter d or \delta; a partial derivative specifically requires \partial.
Examples
$\frac{\partial f}{\partial x}$a first partial derivative
$\frac{\partial^2 f}{\partial x^2}$a second partial
$\frac{\partial^2 f}{\partial x\, \partial y}$a mixed second partial
$\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right)$gradient components
$\partial \Omega$the boundary of a region
Tips and common mistakes
\partialis a symbol, not a function; build the derivative with\frac, e.g.\frac{\partial f}{\partial x}.- For higher orders put the power on
\partialand the variable:\frac{\partial^2 f}{\partial x^2}. - A mixed partial needs a thin space:
\frac{\partial^2 f}{\partial x\,\partial y}. - Never use d or
\deltain place of\partialfor partial derivatives. - Inline, a
\fracpartial can look cramped;\dfrackeeps it full size if readability suffers.
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Convert your maths to LaTeX →FAQ
How do I write a partial derivative in LaTeX?
Use \partial inside a fraction: .
How do I write a second or mixed partial derivative?
Second: \frac{\partial^2 f}{\partial x^2}. Mixed: \frac{\partial^2 f}{\partial x\,\partial y}, with a thin space between the variables.
What is the difference between \partial and d for derivatives?
\partial is for partial derivatives of multivariable functions; the ordinary derivative of a single-variable function uses d, as in \frac{dy}{dx}.