# `∂` — Derivative

Keys: `Alt-f`

`f∂X`: gradient of `f` at `X`. `f` must return a unit. `U f∂ X`:
vector–Jacobian product, where `U` has the shape of `f`’s result. The
result has the shape of `X`.

Currently supports real evaluators `C⌻`, including factored and
exponent-table forms. `C⌻` is a train that binds `C`, the same as `C↣⌻`.

``` bpl
f←[1 2 3]ₓ⌻ ⋄ f∂2ₓ                ⍝ 14ₓ
f←[1 2 3]ₓ⌻ ⋄ f∂∂2ₓ               ⍝ 6ₓ
f←[1 2 3]ₓ⌻ ⋄ [10 20]ₓ f∂ [1 2]ₓ  ⍝ [80 280]ₓ
```

Multivariate gradients retain the coordinate enclosure. A shared unit
coordinate sums partials.

``` bpl
f←⊂[1 2 0⋄1 0 2]ₓ ⌻ ⋄ f∂⊂[3 4]ₓ      ⍝ ⊂[6 8]ₓ
f←⊂[1 2 0⋄1 0 2]ₓ ⌻ ⋄ f∂3ₓ           ⍝ 12ₓ
```

Repeated `∂` requires unit input and output and one variable.

## Errors

- `RANK`: monadic array output
- `LENGTH`: wrong cotangent shape
- `DOMAIN`: unsupported function or nonfinite/non-real data