{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "084NGSTWM7"
    }
  ],
  "body": "\n## Definition\n\nLet $I$ be an open interval and let $f \\colon I \\to \\mathbb{R}$ be [[differentiable|0A61B60B5R]] on $I$.\nThe derivative function of $f$ is the function $f' \\colon I \\to \\mathbb{R}$ that maps each $x \\in I$ to the [[derivative|0F1WR9C83K]] $f'(x)$ of $f$ at $x$.\n\n## Remarks\n\nOther notations are $\\frac{df}{dx}$ and $D f$.\nFor example, the derivative function of $x^3$ is $3 x^2$.\nThe derivative function need not be continuous. See [[x^2 sin(1/x)|0WDAKKN4NC]].\nMathlib defines `deriv f` on all of $\\mathbb{R}$, with value $0$ at points where $f$ is not differentiable.\n\n## Explanations\n\n### L1 human\n\nThe derivative function collects the slopes of $f$ at all points into one new function.\nWe can then differentiate it again.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "defines": "0QKJ6NT0R9",
    "kind": "definition",
    "msc": [
      "26A24"
    ],
    "name": "Derivative function",
    "sources": [
      {
        "locator": "Definition",
        "url": "https://en.wikipedia.org/wiki/Derivative"
      }
    ],
    "tag": "027K9RMZ43",
    "uses": [
      "0F1WR9C83K",
      "0A61B60B5R"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/027K9RMZ43/",
  "links": [
    {
      "field": "defines",
      "target": "0QKJ6NT0R9"
    },
    {
      "field": "uses",
      "target": "0F1WR9C83K"
    },
    {
      "field": "uses",
      "target": "0A61B60B5R"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/027K9RMZ43.md",
  "msc": [
    "26A24"
  ],
  "name": "Derivative function",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/027/027K9RMZ43.md",
  "status": null,
  "tag": "027K9RMZ43",
  "uri": "m2://027K9RMZ43",
  "url": "https://math2.tamnd.com/wiki/derivative-function-definition/",
  "writing": {
    "tag": "027K9RMZ43",
    "kind": "definition",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}