∂

The character ∂ (html element: ∂ or ∂, unicode: U+2202) or $\partial$ is a stylized d mainly used as a mathematical symbol to denote a partial derivative such as ${\frac {\partial z}{\partial x}}$ (read as "the partial derivative of z with respect to x"). The symbol was originally introduced by Legendre in 1786, but only gained popularity when it was used by Jacobi in 1841.^[1]

∂ is also used to denote the following:

• The Jacobian, ${\frac {\partial (x,y,z)}{\partial (u,v,w)}}$.
• The boundary of a set in topology.
• The boundary operator on a chain complex in homological algebra.
• The boundary operator of a differential graded algebra.
• The Dolbeault operator on complex differential forms.

The symbol may be referred to as "del",^[2] "dee",^[3] "partial dee",^[4] "partial", "curly dee",^[5] or "dabba".^[6]

The lowercase Cyrillic De can look similar.

References

1. Aldrich, John. "Earliest Uses of Symbols of Calculus". Retrieved 16 January 2014.
2. Bhardwaj, R.S. (2005), Mathematics for Economics & Business (2nd ed.), p. 6.4
3. Silverman, Richard A. (1989), Essential Calculus: With Applications, p. 216
4. Pemberton, Malcolm; Rau, Nicholas (2011), Mathematics for Economists: An Introductory Textbook, p. 271
5. Bowman, Elizabeth (2014), Video Lecture for University of Alabama in Huntsville
6. Gokhale, Mujumdar, Kulkarni, Singh, Atal, Engineering Mathematics I, p. 10.2, Nirali Prakashan ISBN 8190693549.