{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nLeibniz's notation for the [[derivative|0V1EJCT8G6]], which is used in several slightly different ways.\n\nIf $y$ is a variable that depends on $x$, then $\\textstyle \\frac{\\mathrm{d}y}{\\mathrm{d}x}$, read as \"d $y$ over d $x$\" (commonly shortened to \"d $y$ d $x$\"), is the derivative of $y$ with respect to $x$.\n\nIf $f$ is a [[function|0EPAT51DXQ]] of a single variable $x$, then $\\textstyle \\frac{ \\mathrm{d} f }{ \\mathrm{d}x }$ is the derivative of $f$, and $\\textstyle \\frac{ \\mathrm{d} f }{ \\mathrm{d}x }(a)$ is the value of the derivative at $a$. Sometimes $\\textstyle \\frac{ \\mathrm{d} }{ \\mathrm{d}x }$ is used as a symbol for the derivative operator, which can be prepended to a function: $\\textstyle \\frac{ \\mathrm{d} }{ \\mathrm{d}x } f(x)$.\n\nTotal derivative: If $f(x_1, \\ldots, x_n)$ is a [[function|0EPAT51DXQ]] of several variables that depend on $x$, then $\\textstyle \\frac{\\mathrm{d}f}{\\mathrm{d}x}$ is the derivative of $f$ considered as a function of $x$. That is, $\\textstyle\\ \\frac{\\mathrm{d}f}{\\mathrm{d}x} = \\sum_{i=1}^n \\frac{ \\partial f }{ \\partial x_i }\\ \\frac{\\mathrm{d}x_i}{\\mathrm{d}x} ~.$\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "inventory": [
      "CQ52NZXF9Z"
    ],
    "kind": "concept",
    "name": "Leibnitz",
    "sources": [
      {
        "locator": "Glossary of mathematical symbols, section Calculus",
        "mention": "wikipedia://en/73634#4A02",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:73634@r1376316324"
      }
    ],
    "tag": "9H5Q40RRDH"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/9H5Q40RRDH/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/9H5Q40RRDH.md",
  "msc": null,
  "name": "Leibnitz",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/9H5/9H5Q40RRDH.md",
  "status": null,
  "tag": "9H5Q40RRDH",
  "uri": "m2://9H5Q40RRDH",
  "url": "https://math2.tamnd.com/wiki/leibnitz/",
  "writing": {
    "tag": "9H5Q40RRDH",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}