Quiz — Calculus Early Transcendentals 8th Edition (metric version) by James Stewart (z-lib.org).pdf

Question 1 sur 10 20:00

[{"id":108895,"question":"Quelle est la dérivée de la fonction f(x) = e^(3x) ?","option_a":"3e^(3x)","option_b":"e^(3x)","option_c":"3x e^(3x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x) = 3x, donc u'(x) = 3. Ainsi, f'(x) = 3e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3e^(3x)\", \"b\": \"e^(3x)\", \"c\": \"3x e^(3x)\", \"d\": \"e^(x)\"}}","_debug_options_count":4},{"id":108896,"question":"L'intégrale de f(x) = 1\/x est ln|x| + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est exact : la primitive de 1\/x est ln|x| + C, où C est une constante d'intégration.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":108897,"question":"Quelle est la dérivée de f(x) = ln(5x) ?","option_a":"1\/x","option_b":"5\/x","option_c":"1\/(5x)","option_d":"5\/(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u(x)) est u'(x)\/u(x). Ici, u(x) = 5x, donc u'(x) = 5. Ainsi, f'(x) = 5\/(5x) = 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\/x\", \"b\": \"5\/x\", \"c\": \"1\/(5x)\", \"d\": \"5\/(x)\"}}","_debug_options_count":4},{"id":108898,"question":"L'intégrale de f(x) = sin(x) est -cos(x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est correct : la primitive de sin(x) est -cos(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":108899,"question":"Quelle est la dérivée de f(x) = x^2 * e^x ?","option_a":"2x e^x","option_b":"x^2 e^x + 2x e^x","option_c":"(2x + x^2) e^x","option_d":"x e^x (x + 2)","option_e":"","option_f":"","bonne_reponse":"c","explication":"On utilise la règle du produit : (u*v)' = u'v + uv'. Ici, u = x^2 et v = e^x, donc u' = 2x et v' = e^x. Ainsi, f'(x) = 2x e^x + x^2 e^x = (2x + x^2) e^x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"2x e^x\", \"b\": \"x^2 e^x + 2x e^x\", \"c\": \"(2x + x^2) e^x\", \"d\": \"x ","_debug_options_count":4},{"id":108900,"question":"L'intégrale de f(x) = cos(x) est sin(x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est exact : la primitive de cos(x) est sin(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":108901,"question":"Quelle est la dérivée de f(x) = arctan(x) ?","option_a":"1\/(1 + x^2)","option_b":"1\/(1 - x^2)","option_c":"x\/(1 + x^2)","option_d":"1\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de arctan(x) est 1\/(1 + x^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\": \"1\/(1 + x^2)\", \"b\": \"1\/(1 - x^2)\", \"c\": \"x\/(1 + x^2)\", \"d\": \"1\/x\"}","_debug_options_count":4},{"id":108902,"question":"L'intégrale de f(x) = 1\/(1 + x^2) est arctan(x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est correct : la primitive de 1\/(1 + x^2) est arctan(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":108903,"question":"Quelle est la dérivée de f(x) = x * ln(x) ?","option_a":"ln(x) + 1","option_b":"1\/x","option_c":"x + ln(x)","option_d":"ln(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"On utilise la règle du produit : (u*v)' = u'v + uv'. Ici, u = x et v = ln(x), donc u' = 1 et v' = 1\/x. Ainsi, f'(x) = 1 * ln(x) + x * (1\/x) = ln(x) + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"ln(x) + 1\", \"b\": \"1\/x\", \"c\": \"x + ln(x)\", \"d\": \"ln(x)\"}}","_debug_options_count":4},{"id":108904,"question":"L'intégrale de f(x) = e^x est e^x + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est exact : la primitive de e^x est e^x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]