Quiz : Fonctions trigonométriques et leurs dérivées — Bac Maths

Question 1 sur 10 10:00

[{"id":42606,"question":"Quelle est la dérivée de la fonction f(x) = sin(2x) ?","option_a":"A. cos(2x)","option_b":"B. 2cos(2x)","option_c":"C. -2cos(2x)","option_d":"D. 2sin(2x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"En appliquant la règle de la chaîne, f'(x) = 2 * cos(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42607,"question":"La dérivée de cos(x) est-elle -sin(x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de cos(x) est bien -sin(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42608,"question":"Quelle est la dérivée de f(x) = tan(x) ?","option_a":"A. 1 + tan²(x)","option_b":"B. 1 - tan²(x)","option_c":"C. sec²(x)","option_d":"D. -sec²(x)","option_e":"","option_f":"","bonne_reponse":"C","explication":"La dérivée de tan(x) est sec²(x), car tan(x) = sin(x)\/cos(x) et sa dérivée se calcule par la règle du quotient.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42609,"question":"Si f(x) = cos(3x + π\/4), quelle est f'(x) ?","option_a":"A. -3sin(3x + π\/4)","option_b":"B. -sin(3x + π\/4)","option_c":"C. 3sin(3x + π\/4)","option_d":"D. sin(3x + π\/4)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de la chaîne, f'(x) = -3 * sin(3x + π\/4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42610,"question":"La dérivée de sin²(x) est-elle 2sin(x)cos(x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car sin²(x) = (sin(x))², donc sa dérivée est 2sin(x) * cos(x) par la règle de la chaîne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42611,"question":"Quelle est la dérivée de f(x) = x * sin(x) ?","option_a":"A. sin(x) + xcos(x)","option_b":"B. sin(x) - xcos(x)","option_c":"C. cos(x) + xsin(x)","option_d":"D. cos(x) - xsin(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la règle du produit, f'(x) = sin(x) + x * cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42612,"question":"Si f(x) = arccos(x), quelle est f'(x) ?","option_a":"A. -1\/√(1-x²)","option_b":"B. 1\/√(1-x²)","option_c":"C. -√(1-x²)","option_d":"D. 1\/√(x²-1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de arccos(x) est -1\/√(1-x²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42613,"question":"La dérivée de sin(x) + cos(x) est-elle sin(x) - cos(x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de sin(x) + cos(x) est cos(x) - sin(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42614,"question":"Quelle est la dérivée de f(x) = sin(x²) ?","option_a":"A. 2xcos(x²)","option_b":"B. xcos(x²)","option_c":"C. 2xsin(x²)","option_d":"D. -2xcos(x²)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de la chaîne, f'(x) = 2x * cos(x²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42615,"question":"Si f(x) = tan²(x), quelle est f'(x) ?","option_a":"A. 2tan(x) * sec²(x)","option_b":"B. 2tan(x) * cos²(x)","option_c":"C. tan(x) * sec²(x)","option_d":"D. 2tan(x) * sin²(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la règle de la chaîne et la dérivée de tan(x), f'(x) = 2tan(x) * sec²(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]