# \functionalderivative

Verbose physics-package command for functional or variational derivatives in field theory and variational calculus.

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

## 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`

Verbose physics-package command for functional or variational derivatives in field theory and variational calculus.

## Examples

```latex
\functionalderivative{F}
```

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

```latex
\functionalderivative{F}{x}
```

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

```latex
\functionalderivative[2]{F}
```

[Open in Playground](https://play.texform.dev/?input=%5Cfunctionalderivative%5B2%5D%7BF%7D)

```latex
\functionalderivative*{F}{x}
```

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

→

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

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

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

Collapse long functional derivative names to the fdv command.

Level: authoring. Fidelity: render.

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

→

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

```latex
\functionalderivative{S[\phi]}{\phi(x)}=0
```

→

```latex
\fdv{S[\phi]}{\phi(x)}=0
```

## Equivalent forms

```latex
\fderivative
```

exact. PhysicsMappings registers all three names to the same Derivative handler with argMax=2 and op='\\delta'.

```latex
\fdv
```

exact. PhysicsMappings registers all three names to the same Derivative handler with argMax=2 and op='\\delta'.

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

## Test cases

### physics

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