# Partial Differentiation [Subscript]

1. May 25, 2009

### Air

What does the subscript outside a partial differentiation mean? For example:

$$\left(\frac{\partial x}{\partial y}\right)_z$$

What does the $$z$$ mean above?

2. May 25, 2009

### cristo

Staff Emeritus
It means "holding z constant".

3. Aug 10, 2011

### Amos Axiom

Is that any different from a regular partial derivative though? I've started to encounter the notation in literature and am finding it strange.

4. Aug 11, 2011

### Ray Vickson

It is rarely used in Mathematics, but is used often in some fields such as Thermodynamics. Basically, it indicates that we are considering x to be a function of y and z, without using notation like x(y,z).

RGV