Quiz : Maîtrisez les fonctions dérivées en Terminale Math

Question 1 sur 5 10:00

[{"id":2619,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"3x² - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2620,"question":"Si f(x) = e^(2x), quelle est sa dérivée ?","option_a":"e^(2x)","option_b":"2e^(2x)","option_c":"2x e^(2x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x) = 2x donc u'(x) = 2, d'où f'(x) = 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2621,"question":"Quelle est la dérivée de g(x) = ln(3x + 1) ?","option_a":"1\/(3x + 1)","option_b":"3\/(3x + 1)","option_c":"1\/(x + 1)","option_d":"3\/ln(3x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de ln(u(x)) est u'(x)\/u(x). Ici, u(x) = 3x + 1 donc u'(x) = 3, d'où g'(x) = 3\/(3x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2622,"question":"Soit h(x) = (2x + 1)\/(x - 3). Quelle est sa dérivée ?","option_a":"(2x - 7)\/(x - 3)²","option_b":"(2x - 7)\/(x - 3)","option_c":"(x - 3)\/(2x - 7)","option_d":"2\/(x - 3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"On utilise la formule (u\/v)' = (u'v - uv')\/v². Ici, u = 2x + 1, v = x - 3, u' = 2, v' = 1, donc h'(x) = (2(x-3) - (2x+1))\/(x-3)² = (2x - 6 - 2x - 1)\/(x-3)² = -7\/(x-3)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2623,"question":"Quelle est la dérivée de k(x) = sin(4x) ?","option_a":"cos(4x)","option_b":"4cos(4x)","option_c":"4sin(4x)","option_d":"-4cos(4x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de sin(u(x)) est u'(x) * cos(u(x)). Ici, u(x) = 4x donc u'(x) = 4, d'où k'(x) = 4cos(4x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]