{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.derivative","code":"thing-q29175","url":"https://ver.cy/models/thing/q29175/","name":"derivative","alternateNames":["spectral radiance with respect to frequency","spectral irradiance with respect to frequency","spectral radiant flux","spectral radiant exitance with respect to frequency","spectral linear absorption coefficient","spectral fluence rate","spectral photon exitance","spectral photon flux","spectral photon irradiance","spectral quantity","spectral radiant exitance with respect to wavelength","spectral luminous intensity in terms of frequency"],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"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.","purpose":"Let an agent explain derivatives and compute them, apply derivatives to rates, optimisation and physics, interpret spectral quantities as derivatives, and separate the financial sense.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Limit definition","Local rate of change","Rules of differentiation","Generalisable"],"structure":{"bundles":[{"id":"define","name":"Define","description":"What a derivative is.","layers":[{"id":"definition","name":"Definition","description":"Limit definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"How is the derivative defined as a limit, and how is it interpreted as slope and rate of change?","kind":"definition"},{"text":"Is the calculus sense, a financial derivative or a chemical derivative meant?","kind":"boundary"}]}]},{"id":"rules","name":"Rules","description":"Differentiation rules.","findings":[{"id":"rules-finding","name":"Rules","description":"Rules.","questions":[{"text":"What are the rules for derivatives of sums, products, quotients and compositions?","kind":"definition"},{"text":"What is the derivative of this function?","kind":"action"}]}]}]},{"id":"apply","name":"Apply","description":"Using derivatives.","layers":[{"id":"rates","name":"Rates","description":"Rates and optimisation.","findings":[{"id":"rates-finding","name":"Rates","description":"Rates.","questions":[{"text":"How are derivatives used to find rates of change, extrema and related rates in this problem?","kind":"action"},{"text":"How is a function analysed using its derivatives?","kind":"action"}]}]},{"id":"physics","name":"Physics","description":"Derivatives in science.","findings":[{"id":"physics-finding","name":"Physics","description":"Science.","questions":[{"text":"How do velocity, acceleration and other physical quantities arise as derivatives?","kind":"definition"},{"text":"What are spectral quantities such as spectral radiance with respect to frequency, and why do they differ per wavelength?","kind":"definition"}]}]}]},{"id":"extend","name":"Extend","description":"Beyond one variable.","layers":[{"id":"partial","name":"Partial","description":"Partial and directional derivatives.","findings":[{"id":"partial-finding","name":"Partial","description":"Partial derivatives.","questions":[{"text":"What are partial, directional and total derivatives, and how are gradients used?","kind":"definition"},{"text":"How are they computed for this function?","kind":"action"}]}]},{"id":"numeric","name":"Numeric","description":"Numerical differentiation.","findings":[{"id":"numeric-finding","name":"Numeric","description":"Numerical.","questions":[{"text":"How are derivatives approximated numerically and computed by automatic differentiation?","kind":"definition"},{"text":"What errors arise?","kind":"boundary"}]}]}]},{"id":"learn","name":"Learn","description":"Teaching and history.","layers":[{"id":"teach","name":"Teach","description":"Teaching derivatives.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can derivatives be taught with graphs and motion examples?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]},{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did Newton, Leibniz and later mathematicians develop the derivative?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Compute derivatives and explain them as rates of change or slopes of tangents.","Distinguish the calculus derivative from financial derivatives."],"mustNot":["Confuse a derivative with a finite difference without noting the approximation.","Present a derivative as existing where the function is not differentiable.","Give students worked answers presented as their own work in assessed tasks."],"requiresHuman":["Grading students' work in calculus."]},"ethics":{"considerations":["Students depend on correct explanations; errors compound in later study.","Models built on derivatives drive engineering and economic decisions."],"affectedParties":["Students and teachers","Engineers and analysts"]},"owners":{"steward":"Nobody owns the concept; it belongs to mathematics and is held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q11348","type":"parent","note":"registry parent class"},{"target":"Q137924178","type":"parent","note":"registry parent class"},{"target":"function","type":"related","note":"category"},{"target":"rate of change","type":"related","note":"category"},{"target":"sum","type":"related","note":"Riemann sums and integrals"},{"target":"acceleration","type":"related","note":"derivative of velocity"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.derivative","Wikidata: Q29175 (https://www.wikidata.org/wiki/Q29175)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Rate of change of a function","Slope of the tangent","A financial derivative is a contract, not a rate","Not physical; slopes of curves and formulas."]},"capabilities":{"applicability":"required","items":["explain and compute derivatives","apply to rates and optimisation","interpret spectral derivatives","separate other senses"]},"hazards":{"applicability":"required","items":["Confusing derivative with difference or with financial derivatives","Differentiation rule errors","Misinterpreting spectral quantities per frequency versus per wavelength"]},"interfaces":{"applicability":"required","items":["Mathematical notation conventions","Radiometric quantity definitions for spectral derivatives"]},"context":{"applicability":"required","items":["Rates of change of functions.","ordinary derivatives","partial and directional derivatives","higher-order derivatives","spectral derivatives such as spectral radiance","derivatives in vector calculus"]}},"sources":[{"title":"Wikidata item Q29175: derivative","url":"https://www.wikidata.org/wiki/Q29175","note":"identity and sense of the item"},{"title":"Wikipedia: Derivative","url":"https://en.wikipedia.org/wiki/Derivative","note":"general description of the item"}],"openQuestions":["Should differentiation rules be a separate entry?","How should calculus resources be linked?","How should radiometric definitions be linked?"],"resources":{"spec":"/models/things/publications/thing-q29175/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q29175/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T22:57:41Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:51:58+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}