Partial derivative symbol (∂)
∂ is the partial derivative sign, a rounded d. ∂f/∂x, read “the partial of f with respect to x”, is the rate at which f changes with x when every other variable is held constant.
Easily confused with
How to read it
OpenStax’s Calculus Volume 3 brings it in for functions of more than one variable: Leibniz’s notation dy/dx is kept, but the d is replaced with ∂, and the partial derivative of f with respect to x can also be written fₓ. OpenStax says the rounded d is usually called “partial”, and the rule it gives is to treat every independent variable except the one being differentiated as a constant. The IUPAC Green Book lists three ways of writing it: ∂f/∂x, ∂ₓf and Dₓf. Unicode names the character ∂ (U+2202) PARTIAL DIFFERENTIAL.
Also searched as: ∂, curly d, del symbol, Jacobi’s delta, partial derivative symbol symbol, partial symbol, round d, ∂/∂x.
Look-alikes
∂ is a rounded Latin d, not the Greek small delta δ, in spite of the name Jacobi’s delta. It is also not ∇, the nabla, read “del”, which has a page of its own.
Read next
- Next in Physics and chemistry symbolsVector arrow and hat (v⃗, x̂)An arrow over a letter, v⃗, marks a vector: a quantity with a direction as well as a size. A hat, x̂, marks a unit vector, which has length one and gives only a direction; î, ĵ and k̂ point along the x, y and z axes.
- ∇, read del, is the other operator of vector calculus.Nabla (∇)Nabla (∇) is an upside-down triangle used in vector calculus for the del operator: ∇f is the gradient of a function f, read “del f”. It is not a Greek letter, though it is shaped like an inverted capital delta, Δ.
More physics and chemistry symbols
The same shape elsewhere
Browse symbols drawn with curves and waves or letters and numbers.
Sources
- Mathematical Operators: Range 2200–22FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Mathematical Operators, 2202
- Calculus Volume 3, 4.3 Partial Derivatives, OpenStax (Rice University), Derivatives of a Function of Two Variables; Definition
- Earliest Uses of Symbols of Calculus, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Partial derivative
- Quantities, Units and Symbols in Physical Chemistry (the Green Book), IUPAC Green Book, 3rd edition, 2nd printing (2008), International Union of Pure and Applied Chemistry (IUPAC), Sec. 4.2 Symbols, operators and functions
Researched, edited and approved by Rory Hansen before publishing. Last reviewed October 9, 2026. How we research
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