∂ Partial derivative

Say it: “the partial derivative of f with respect to x”, “partial f partial x”, “del f del x”

What it means

A curly d marks a partial derivative: how a function of several variables changes when one of them changes and the others are held fixed.

Calculus

∂f/∂x = 2x

Aethel says

the partial derivative of f with respect to x equals 2x

f's rate of change in the x direction

Physics

∂²u/∂t² = c² ∇²u

Aethel says

the second partial derivative of u with respect to t equals c squared times the Laplacian of u

the wave equation

Schrödinger equation

iħ ∂ψ/∂t = Ĥψ

Faraday's law of induction

∇ × E = −∂B/∂t

Wave equation

∂²u/∂t² = c² ∇²u

Navier–Stokes equation

ρ(∂u/∂t + u · ∇u) = −∇p + μ∇²u + f

How do you say ∂ out loud?

It is usually read “the partial derivative of f with respect to x”, and also “partial f partial x” or “del f del x”.

What does ∂ mean in maths?

A curly d marks a partial derivative: how a function of several variables changes when one of them changes and the others are held fixed.

How do you type ∂?

In LaTeX, write \partial. Its Unicode code point is U+2202.

What is ∂ often confused with?

It is easy to mistake for the Greek letter δ, and the Latin d of an ordinary derivative.