{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "06SKCHDQT5"
    },
    {
      "field": "uses",
      "target": "0HFSFVMWQB"
    },
    {
      "field": "uses",
      "target": "0K9QCK6WJC"
    },
    {
      "field": "uses",
      "target": "0Y9D2FJRQ4"
    }
  ],
  "body": "\n## Definition\n\nLet $I$ be an open interval and let $f \\colon I \\to \\mathbb{R}$.\nLet $f^{(0)} = f$.\nIf $f^{(n)}$ is defined and differentiable on $I$, let $f^{(n+1)} = (f^{(n)})'$, its [[derivative function|027K9RMZ43]].\nThe function $f^{(n)}$ is the $n$-th derivative of $f$, and $f$ is $n$ times differentiable when it exists.\n\n## Remarks\n\nThe [[second derivative|0Y9D2FJRQ4]] is $f'' = f^{(2)}$.\nFor example, the $n$-th derivative of $x^n$ is the constant $n!$.\nMathlib defines `iteratedDeriv n f`.\n\n## Explanations\n\n### L1 human\n\nHigher derivatives come from differentiating again and again.\nThey describe finer features of a function, like the bending of its graph.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "defines": "04TKTF8KDK",
    "kind": "definition",
    "msc": [
      "26A24"
    ],
    "name": "Higher derivative",
    "sources": [
      {
        "locator": "Higher-order derivatives",
        "url": "https://en.wikipedia.org/wiki/Derivative"
      }
    ],
    "tag": "084NGSTWM7",
    "uses": [
      "027K9RMZ43"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/084NGSTWM7/",
  "links": [
    {
      "field": "defines",
      "target": "04TKTF8KDK"
    },
    {
      "field": "uses",
      "target": "027K9RMZ43"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/084NGSTWM7.md",
  "msc": [
    "26A24"
  ],
  "name": "Higher derivative",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/084/084NGSTWM7.md",
  "status": null,
  "tag": "084NGSTWM7",
  "uri": "m2://084NGSTWM7",
  "url": "https://math2.tamnd.com/wiki/higher-derivative-definition/",
  "writing": {
    "tag": "084NGSTWM7",
    "kind": "definition",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}