{
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    "definition": "In calculus, the rate at which a function changes with respect to its variable, defined as the limit of the difference quotient and interpreted as the slope of the tangent or the instantaneous rate of change, with rules for computing derivatives of sums, products, quotients and compositions, and extensions to partial, directional and higher derivatives; in physics and engineering, spectral quantities such as spectral radiance are derivatives with respect to frequency or wavelength.",
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      "A financial derivative is a contract, not a rate"
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        "relation": "is a kind of",
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      {
        "relation": "is related to",
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      {
        "relation": "is related to",
        "target": "acceleration",
        "why": "derivative of velocity"
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    "identifiers": [],
    "standards_and_regulation": [
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      "Radiometric quantity definitions for spectral derivatives"
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      "Confusing derivative with difference or with financial derivatives",
      "Differentiation rule errors",
      "Misinterpreting spectral quantities per frequency versus per wavelength"
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    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
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        "Present a derivative as existing where the function is not differentiable.",
        "Give students worked answers presented as their own work in assessed tasks."
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    "owners": {
      "steward": "Nobody owns the concept; it belongs to mathematics and is held in common.",
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        "name": "Define",
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                    "text": "Is the calculus sense, a financial derivative or a chemical derivative meant?",
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                    "text": "What is the derivative of this function?",
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                "questions": [
                  {
                    "text": "How are derivatives used to find rates of change, extrema and related rates in this problem?",
                    "kind": "action"
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                    "text": "How is a function analysed using its derivatives?",
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                  }
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              }
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                    "text": "How do velocity, acceleration and other physical quantities arise as derivatives?",
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                    "text": "What are spectral quantities such as spectral radiance with respect to frequency, and why do they differ per wavelength?",
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              }
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                    "text": "What are partial, directional and total derivatives, and how are gradients used?",
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                  {
                    "text": "How are they computed for this function?",
                    "kind": "action"
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              }
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                    "text": "How are derivatives approximated numerically and computed by automatic differentiation?",
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                    "text": "What errors arise?",
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                    "text": "How can derivatives be taught with graphs and motion examples?",
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                    "text": "Which misconceptions arise?",
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                    "text": "How did Newton, Leibniz and later mathematicians develop the derivative?",
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                    "text": "Which references are standard?",
                    "kind": "provenance"
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  "openQuestions": [
    "Should differentiation rules be a separate entry?",
    "How should calculus resources be linked?",
    "How should radiometric definitions be linked?"
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