# \partialderivative

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

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

## Metadata

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

## Syntax

### physics

Argument specification: `s o m g g`

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

## Examples

```latex
\partialderivative{f}
```

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

```latex
\partialderivative{f}{x}
```

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

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

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

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

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

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

[Open in Playground](https://play.texform.dev/?input=%5Cpartialderivative*%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
\partialderivative{#1}{#2}
```

→

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

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

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

Collapse long partial derivative names to the pdv command.

Level: authoring. Fidelity: render.

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

→

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

```latex
J=\pderivative{f}{x}+\pderivative{g}{y}
```

→

```latex
J=\pdv{f}{x}+\pdv{g}{y}
```

## Equivalent forms

```latex
\pderivative
```

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

```latex
\pdv
```

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)
- [\\pderivative](https://texform.dev/latex/commands/pderivative)
- [\\pdv](https://texform.dev/latex/commands/pdv)

## Test cases

### physics

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