# physics/partial-derivative-to-pdv

Collapse long partial derivative names to the pdv command.

https://texform.dev/rules/physics/partial-derivative-to-pdv

## Metadata

| Field | Value |
| --- | --- |
| Key | physics/partial-derivative-to-pdv |
| Level | authoring |
| Fidelity | render |
| Enabled by packages | physics |
| Profiles | Authoring, Faithful, Corpus, Equiv |

## Rewrite patterns

### partialderivative-two-args

From:

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

To:

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

### partialderivative-star

From:

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

To:

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

### partialderivative-order

From:

```latex
\partialderivative[#1]{#2}{#3}
```

To:

```latex
\pdv[#1]{#2}{#3}
```

### partialderivative-single-arg

From:

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

To:

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

### partialderivative-three-args

From:

```latex
\partialderivative{#1}{#2}{#3}
```

To:

```latex
\pdv{#1}{#2}{#3}
```

### pderivative-two-args

From:

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

To:

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

### pderivative-star

From:

```latex
\pderivative*{#1}{#2}
```

To:

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

### pderivative-order

From:

```latex
\pderivative[#1]{#2}{#3}
```

To:

```latex
\pdv[#1]{#2}{#3}
```

### pderivative-single-arg

From:

```latex
\pderivative{#1}
```

To:

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

### pderivative-three-args

From:

```latex
\pderivative{#1}{#2}{#3}
```

To:

```latex
\pdv{#1}{#2}{#3}
```

## Examples

Examples show the rule in isolation, not a complete normalization profile.

### pdv alias jacobian entry

Before:

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

After this rule:

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

Packages: base, physics.

Rendering verified with the declared packages.

### partialderivative long alias

Before:

```latex
\partialderivative{T}{z}=0
```

After this rule:

```latex
\pdv{T}{z}=0
```

Packages: base, physics.

Rendering verified with the declared packages.

### partialderivative star alias

Before:

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

After this rule:

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

Packages: base, physics.

Rendering verified with the declared packages.

### partialderivative order alias

Before:

```latex
\partialderivative[n]{f}{x}
```

After this rule:

```latex
\pdv[n]{f}{x}
```

Packages: base, physics.

Rendering verified with the declared packages.

### partialderivative single arg alias

Before:

```latex
\partialderivative{x} f(x,y)
```

After this rule:

```latex
\pdv{x} f(x,y)
```

Packages: base, physics.

Rendering verified with the declared packages.

### partialderivative mixed alias

Before:

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

After this rule:

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

Packages: base, physics.

Rendering verified with the declared packages.

### pderivative star alias

Before:

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

After this rule:

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

Packages: base, physics.

Rendering verified with the declared packages.

### pderivative order alias

Before:

```latex
\pderivative[n]{f}{x}
```

After this rule:

```latex
\pdv[n]{f}{x}
```

Packages: base, physics.

Rendering verified with the declared packages.

### pderivative single arg alias

Before:

```latex
\pderivative{x} f(x,y)
```

After this rule:

```latex
\pdv{x} f(x,y)
```

Packages: base, physics.

Rendering verified with the declared packages.

### pderivative mixed alias

Before:

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

After this rule:

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

Packages: base, physics.

Rendering verified with the declared packages.

## Triggers

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

## Eliminates

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

## Produces

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

## Downstream

- [physics/pdv-to-frac-partial](https://texform.dev/rules/physics/pdv-to-frac-partial): Expand pdv forms to explicit partial-derivative fractions.

## Same family

- [physics/derivative-to-dv](https://texform.dev/rules/physics/derivative-to-dv): Collapse derivative to the compact dv command.
- [physics/functional-derivative-to-fdv](https://texform.dev/rules/physics/functional-derivative-to-fdv): Collapse long functional derivative names to the fdv command.
- [physics/vectorarrow-to-va](https://texform.dev/rules/physics/vectorarrow-to-va): Collapse vectorarrow to the short va helper.
- [physics/vectorbold-to-vb](https://texform.dev/rules/physics/vectorbold-to-vb): Collapse vectorbold to the short vb helper.
- [physics/vectorunit-to-vu](https://texform.dev/rules/physics/vectorunit-to-vu): Collapse vectorunit to the short vu helper.
- [physics/dv-to-frac-d](https://texform.dev/rules/physics/dv-to-frac-d): Expand dv forms to explicit d-based derivative fractions.
- [physics/fdv-to-frac-delta](https://texform.dev/rules/physics/fdv-to-frac-delta): Expand fdv forms to explicit delta-based derivative fractions.
- [physics/pdv-to-frac-partial](https://texform.dev/rules/physics/pdv-to-frac-partial): Expand pdv forms to explicit partial-derivative fractions.
- [physics/va-to-vec-mathbf](https://texform.dev/rules/physics/va-to-vec-mathbf): Canonicalize va to an explicit vec-wrapped mathbf form.
- [physics/vb-to-mathbf](https://texform.dev/rules/physics/vb-to-mathbf): Canonicalize vb to an explicit mathbf wrapper.
- [physics/vu-to-hat-mathbf](https://texform.dev/rules/physics/vu-to-hat-mathbf): Canonicalize vu to an explicit hat-wrapped mathbf form.

## Notes

Alias rewrite: partialderivative, pderivative, and pdv share the same physics Derivative handler and argspec, so star, optional order, one-argument, and mixed-partial forms are preserved by renaming the command. The optional order branch is intentionally represented with two braced arguments because MathJax ignores that order when more derivative variables are supplied.

## Disable this rule

```python
TransformEngine(profile="corpus", disable_rules=["physics/partial-derivative-to-pdv"])
```

```javascript
new TransformEngine({ profile: 'corpus', disableRules: ['physics/partial-derivative-to-pdv'] })
```

[Open in Playground](https://play.texform.dev/?input=J%3D%5Cpderivative%7Bf%7D%7Bx%7D%2B%5Cpderivative%7Bg%7D%7By%7D)