{
  "aliases": [
    "higher-frechet-derivative",
    "kth-derivative"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "0EY05Z9RPN"
    }
  ],
  "body": "\n## Summary\n\nThe iterated derivative $D^k f$ of a map $f$ is the derivative of the derivative, taken $k$ times.\nThe [[Fréchet derivative|06EH97V2A7]] of $D^{k-1} f$ at a point is a linear map with values in $(k-1)$-linear maps, which is the same as a $k$-linear map.\nSo $D^k f(a)$ is a $k$-linear map, and for a function on $\\mathbb{R}^n$ its values on basis vectors are the partial derivatives of order $k$.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "aliases": [
      "higher-frechet-derivative",
      "kth-derivative"
    ],
    "kind": "concept",
    "msc": [
      "26B05"
    ],
    "name": "Iterated derivative",
    "sources": [
      {
        "locator": "Higher derivatives",
        "url": "https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative"
      }
    ],
    "tag": "0F32S73FJN",
    "uses": [
      "06EH97V2A7"
    ]
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0F32S73FJN/",
  "links": [
    {
      "field": "uses",
      "target": "06EH97V2A7"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0F32S73FJN.md",
  "msc": [
    "26B05"
  ],
  "name": "Iterated derivative",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0F3/0F32S73FJN.md",
  "status": null,
  "tag": "0F32S73FJN",
  "uri": "m2://0F32S73FJN",
  "url": "https://math2.tamnd.com/wiki/iterated-derivative/",
  "writing": {
    "tag": "0F32S73FJN",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}