{"version":3,"file":"1F10-jD5lXCKc.js","sources":["../../src/exercices/1e/1F10.js"],"sourcesContent":["import { combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { ecritureAlgebrique, ecritureAlgebriqueSauf1, rienSi1 } from '../../lib/outils/ecritures'\nimport { lettreMinusculeDepuisChiffre } from '../../lib/outils/outilString.js'\nimport Exercice from '../deprecatedExercice.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { simplify, parse, derivative } from 'mathjs'\nconst math = { simplify, parse, derivative }\nexport const titre = 'Calculs de dérivées'\n\n/**\n * Calculs de dérivés\n * @author Rémi Angot\n * Référence 1F10\n*/\nexport const uuid = '2af1c'\nexport const ref = '1F10'\nexport default function CalculsDeDerives () {\n  Exercice.call(this) // Héritage de la classe Exercice()\n  this.titre = titre\n  this.consigne = \"Pour chacune des fonctions suivantes, dire sur quel ensemble elle est dérivable, puis déterminer l'expression de sa fonction dérivée.\"\n  this.nbQuestions = 6\n  this.nbCols = 2 // Nombre de colonnes pour la sortie LaTeX\n  this.nbColsCorr = 2 // Nombre de colonnes dans la correction pour la sortie LaTeX\n  this.sup = 1\n  // On modifie les règles de simplifications par défaut de math.js pour éviter 10x+10 = 10(x+1) et -4x=(-4x)\n  const reglesDeSimplifications = math.simplify.rules.slice()\n  reglesDeSimplifications.splice(reglesDeSimplifications.findIndex(rule => rule.l === 'n1*n2 + n2'), 1)\n  reglesDeSimplifications.splice(reglesDeSimplifications.findIndex(rule => rule.l === 'n1*n3 + n2*n3'), 1)\n  //    reglesDeSimplifications.push({l:\"-(n1*v^2)\",r:\"-n1*v^2\"})\n  this.nouvelleVersion = function () {\n    this.sup = Number(this.sup)\n    this.listeQuestions = [] // Liste de questions\n    this.listeCorrections = [] // Liste de questions corrigées\n    this.liste_valeurs = [] // Les questions sont différentes du fait du nom de la fonction, donc on stocke les valeurs\n\n    let listeTypeDeQuestionsDisponibles\n    if (this.sup === 1) {\n      listeTypeDeQuestionsDisponibles = ['ax+b', 'a', 'ax2+bx+c', 'xn', 'xn+xm', '1/x', 'xn+1/x', '1/xn', 'xn+1/xm', 'racine(x)']\n    } else if (this.sup === 2) {\n      listeTypeDeQuestionsDisponibles = ['ax+b', 'axn', 'a/x', 'a/xn', 'racine(ax)']\n    } else {\n      listeTypeDeQuestionsDisponibles = ['ax+b', 'axn', 'a/x', 'a/xn', 'racine(ax)']\n    }\n    const listeTypeDeQuestions = combinaisonListes(listeTypeDeQuestionsDisponibles, this.nbQuestions)\n\n    for (let i = 0, texte, texteCorr, a, b, c, n, m, expression, ensembleDerivation, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n      switch (listeTypeDeQuestions[i]) {\n        case 'a':\n          a = randint(-10, 10, 0)\n          expression = `${a}`\n          ensembleDerivation = '\\\\mathbb{R}'\n          break\n        case 'ax+b':\n          a = randint(-10, 10, 0)\n          b = randint(-10, 10, 0)\n          expression = `${a}x  ${ecritureAlgebrique(b)}`\n          ensembleDerivation = '\\\\mathbb{R}'\n          break\n        case 'ax2+bx+c':\n          a = randint(-10, 10, 0)\n          b = randint(-10, 10, 0)\n          c = randint(-10, 10, 0)\n          expression = `${rienSi1(a)} x^2  ${ecritureAlgebriqueSauf1(b)} x  ${ecritureAlgebrique(c)}`\n          ensembleDerivation = '\\\\mathbb{R}'\n          break\n        case 'xn':\n          n = randint(2, 10)\n          expression = `x^${n}`\n          ensembleDerivation = '\\\\mathbb{R}'\n          break\n        case 'xn+1/x':\n          n = randint(2, 10)\n          expression = `x^${n}+1/x`\n          ensembleDerivation = '\\\\mathbb{R}^{\\\\text{*}}'\n          break\n        case 'xn+1/xm':\n          n = randint(2, 10)\n          m = randint(2, 10, m)\n          expression = `x^${n}+1/x^${m}`\n          ensembleDerivation = '\\\\mathbb{R}^{\\\\text{*}}'\n          break\n        case 'xn+xm':\n          n = randint(2, 10)\n          m = randint(2, 10, m)\n          expression = `x^${n}+x^${m}`\n          ensembleDerivation = '\\\\mathbb{R}'\n          break\n        case 'axn':\n          a = randint(-10, 10, [0, 1, -1])\n          n = randint(2, 10)\n          expression = `${a}x^${n}`\n          ensembleDerivation = '\\\\mathbb{R}'\n          break\n        case '1/x':\n          expression = '1/x'\n          ensembleDerivation = '\\\\mathbb{R}^{\\\\text{*}}'\n          break\n        case 'a/x':\n          a = randint(-10, 10, [0, 1])\n          expression = `${a}/x`\n          ensembleDerivation = '\\\\mathbb{R}^{\\\\text{*}}'\n          break\n        case '1/xn':\n          n = randint(2, 10)\n          expression = `${1}/x^${n}`\n          ensembleDerivation = '\\\\mathbb{R}^{\\\\text{*}}'\n          break\n        case 'a/xn':\n          a = randint(-10, 10, [1, 0])\n          n = randint(2, 10)\n          expression = `${a}/x^${n}`\n          ensembleDerivation = '\\\\mathbb{R}^{\\\\text{*}}'\n          break\n        case 'racine(x)':\n          expression = 'sqrt(x)'\n          ensembleDerivation = ']0,+\\\\infty['\n          break\n        case 'racine(ax)':\n          a = randint(2, 10, [4, 9])\n          expression = `sqrt(${rienSi1(a)}x)`\n          ensembleDerivation = ']0,+\\\\infty['\n          break\n      }\n\n      texte = `$${lettreMinusculeDepuisChiffre(i + 6)}:x\\\\longmapsto ${math.parse(expression).toTex({ implicit: 'hide' }).replaceAll('\\\\cdot', '')}$`\n      texteCorr = `$${lettreMinusculeDepuisChiffre(i + 6)}$ est dérivable sur $${ensembleDerivation}$ et $ ${lettreMinusculeDepuisChiffre(i + 6)}':x\\\\longmapsto ${math.simplify(math.derivative(expression, 'x'), reglesDeSimplifications).toTex({ implicit: 'hide' }).replaceAll('\\\\cdot', '')}$`\n\n      texte = texte.replaceAll('frac', 'dfrac')\n      texteCorr = texteCorr.replaceAll('frac', 'dfrac')\n\n      if (this.liste_valeurs.indexOf(expression) === -1) {\n        this.liste_valeurs.push(expression)\n        this.listeQuestions.push(texte)\n        this.listeCorrections.push(texteCorr)\n        i++\n      }\n      cpt++\n    }\n    listeQuestionsToContenu(this)\n  }\n  this.besoinFormulaireNumerique = ['Niveau de difficulté', 2, '1 : Fonctions de base \\n2 : ku'] // \\n3 : u/v, 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