# \pdv

Shorthand physics-package command for partial derivatives, including mixed partials and higher-order forms.

https://texform.dev/latex/commands/pdv

## Metadata

| Field | Value |
| --- | --- |
| Topic | [Physics: derivatives](https://texform.dev/latex/topics/physics-derivatives) |
| Packages | physics |
| Allowed mode | math |
| Tags |  |
| Commonality | medium |
| Kind | prefix |

## Syntax

### physics

Argument specification: `s o m g g`

Shorthand physics-package command for partial derivatives, including mixed partials and higher-order forms.

## Examples

```latex
\pdv{f}
```

[Open in Playground](https://play.texform.dev/?input=%5Cpdv%7Bf%7D)

```latex
\pdv{f}{x}
```

[Open in Playground](https://play.texform.dev/?input=%5Cpdv%7Bf%7D%7Bx%7D)

```latex
\pdv{f}{x}{y}
```

[Open in Playground](https://play.texform.dev/?input=%5Cpdv%7Bf%7D%7Bx%7D%7By%7D)

```latex
\pdv[3]{f}
```

[Open in Playground](https://play.texform.dev/?input=%5Cpdv%5B3%5D%7Bf%7D)

```latex
\pdv*{f}{x}
```

[Open in Playground](https://play.texform.dev/?input=%5Cpdv*%7Bf%7D%7Bx%7D)

## Renderer support

| Package | MathJax | KaTeX | XeTeX |
| --- | --- | --- | --- |
| physics | full | none | full |

## In TeXForm

TeXForm parses this entry as prefix syntax; the package determines its argument specification.

### Expands to (physics)

```latex
\pdv{#1}{#2}
```

→

```latex
\frac{\partial #1}{\partial #2}
```

Internal reparse. Star uses \flatfrac. Single argument expands to \frac{\partial}{\partial #1}.

### [physics/pdv-to-frac-partial](https://texform.dev/rules/physics/pdv-to-frac-partial)

Expand pdv forms to explicit partial-derivative fractions.

Level: faithful. Fidelity: render.

```latex
\pdv{#1}{#2}
```

→

```latex
\frac{\partial #1}{\partial #2}
```

```latex
\lambda=\pdv{f}{x}
```

→

```latex
\lambda=\frac{\partial f}{\partial x}
```

## Equivalent forms

```latex
\partialderivative
```

exact. PhysicsMappings registers all three names to the same Derivative handler with argMax=3 and op='\\partial'.

```latex
\pderivative
```

exact. PhysicsMappings registers all three names to the same Derivative handler with argMax=3 and op='\\partial'.

## See also

- [\\derivative](https://texform.dev/latex/commands/derivative)
- [\\dv](https://texform.dev/latex/commands/dv)
- [\\fderivative](https://texform.dev/latex/commands/fderivative)
- [\\fdv](https://texform.dev/latex/commands/fdv)
- [\\functionalderivative](https://texform.dev/latex/commands/functionalderivative)
- [\\partialderivative](https://texform.dev/latex/commands/partialderivative)
- [\\pderivative](https://texform.dev/latex/commands/pderivative)

## Test cases

### physics

| Input | Case | MathJax | KaTeX | XeTeX |
| --- | --- | --- | --- | --- |
| \pdv{a} | Positive: baseline | Pass | Fail | Pass |
| \pdv*{a} | Positive: vary:s[0] | Pass | Fail | Pass |
| \pdv[a]{b} | Positive: vary:o[1] | Pass | Fail | Pass |
| \pdv{a}{b} | Positive: vary:g[3] | Pass | Fail | Pass |
| \pdv*[a]{b}{c}{d} | Positive: maximal | Pass | Fail | Pass |
| \pdv a | Positive: bare[2] | Pass | Fail | Pass |