Quiz — 6657359d1c58f_Corrigé-Revision.pdf

Question 1 sur 5 10:00

[{"id":2050,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6x - 5\", \"b\": \"3x - 5\", \"c\": \"6x² - 5\", \"d\": \"3x² - 5\"}}","_debug_options_count":4},{"id":2051,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"e^(2x)\", \"b\": \"2e^(2x)\", \"c\": \"2x e^(2x)\", \"d\": \"e^(x)\"}}","_debug_options_count":4},{"id":2052,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/(3x + 1)\", \"b\": \"3\/(3x + 1)\", \"c\": \"1\/(x + 1)\", \"d\": \"3\/ln(3x +","_debug_options_count":4},{"id":2053,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(2x - 7)\/(x - 3)²\", \"b\": \"(2x - 7)\/(x - 3)\", \"c\": \"(x - 3)\/(2x -","_debug_options_count":4},{"id":2054,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"cos(4x)\", \"b\": \"4cos(4x)\", \"c\": \"4sin(4x)\", \"d\": \"-4cos(4x)\"}}","_debug_options_count":4}]