Maîtrisez les fonctions dérivées — Quiz interactif pour Terminale Math

Question 1 sur 10 10:00

[{"id":65152,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65153,"question":"La dérivée de f(x) = e^(2x) est f'(x) = 2e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai : la dérivée d'une fonction exponentielle composée est f'(x) = u'(x) × e^(u(x)), ici u(x) = 2x donc u'(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65154,"question":"Quelle est la dérivée de f(x) = ln(3x + 1) ?","option_a":"3\/(3x+1)","option_b":"1\/(3x+1)","option_c":"3x\/(3x+1)","option_d":"1\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u) est u'\/u. Ici u = 3x + 1, donc u' = 3, d'où f'(x) = 3\/(3x+1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65155,"question":"Si f'(x) \u003E 0 sur un intervalle, alors f est décroissante sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux : si f'(x) \u003E 0, alors f est croissante. Si f'(x) \u003C 0, f est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65156,"question":"Quelle est la dérivée de f(x) = sin(5x) ?","option_a":"5cos(5x)","option_b":"cos(5x)","option_c":"sin(5x)","option_d":"5sin(5x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de sin(u) est u'cos(u). Ici u = 5x, donc u' = 5, d'où f'(x) = 5cos(5x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65157,"question":"La dérivée de f(x) = √x est-elle f'(x) = 1\/(2√x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai : la dérivée de √x = x^(1\/2) est (1\/2)x^(-1\/2) = 1\/(2√x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65158,"question":"Quelle est la dérivée de f(x) = (2x + 1)\/(x - 3) ?","option_a":"2\/(x-3)²","option_b":"(x+7)\/(x-3)²","option_c":"2\/(x-3)","option_d":"(2x+1)\/(x-3)","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise la formule de dérivation d'un quotient : (u\/v)' = (u'v - uv')\/v². Ici u = 2x+1, v = x-3, donc u' = 2, v' = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65159,"question":"Si f'(a) = 0, alors la tangente à la courbe de f en x = a est parallèle à l'axe des abscisses.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai : une dérivée nulle en un point signifie que la pente de la tangente est nulle, donc elle est horizontale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65160,"question":"Quelle est la dérivée de f(x) = x³ - 4x² + 5x - 2 ?","option_a":"3x² - 8x + 5","option_b":"3x² - 8x - 2","option_c":"x³ - 4x² + 5","option_d":"3x² - 4x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"On dérive terme à terme : (x³)' = 3x², (-4x²)' = -8x, (5x)' = 5, et (-2)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65161,"question":"La dérivée d'une fonction constante est toujours nulle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai : une fonction constante f(x) = k a une dérivée f'(x) = 0 pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]