Quiz interactif : Dérivées et Primitives — Terminale Math

Question 1 sur 10 10:00

[{"id":26368,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 5x - 2 ?","option_a":"6x + 5","option_b":"6x² + 5","option_c":"3x + 5","option_d":"6x + 5x - 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de puissance : f'(x) = 6x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26369,"question":"La dérivée de sin(x) est cos(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale des fonctions trigonométriques : d\/dx [sin(x)] = cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26370,"question":"Quelle est la primitive de f(x) = 4x³ ?","option_a":"x⁴ + C","option_b":"12x² + C","option_c":"x⁴\/4 + C","option_d":"4x⁴ + C","option_e":"","option_f":"","bonne_reponse":"C","explication":"La primitive de x^n est x^(n+1)\/(n+1) + C. Ici, n=3, donc la primitive est x⁴\/4 + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26371,"question":"La dérivée de e^(2x) est 2e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de la chaîne, d\/dx [e^(2x)] = 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26372,"question":"Quelle méthode utilise-t-on pour trouver une primitive de 1\/(1+x²) ?","option_a":"Intégration par parties","option_b":"Changement de variable","option_c":"Formule standard","option_d":"Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"C","explication":"La primitive de 1\/(1+x²) est arctan(x) + C, une formule standard à connaître.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26373,"question":"La dérivée de ln(x) est 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale : d\/dx [ln(x)] = 1\/x pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26374,"question":"Quelle est la dérivée de f(x) = (2x + 1)³ ?","option_a":"3(2x + 1)²","option_b":"6(2x + 1)²","option_c":"6x(2x + 1)²","option_d":"2(2x + 1)²","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la règle de la chaîne : f'(x) = 3(2x + 1)² * 2 = 6(2x + 1)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26375,"question":"La primitive de 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 une propriété fondamentale : ∫cos(x) dx = sin(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26376,"question":"Quelle est la dérivée de f(x) = √(x) ?","option_a":"1\/(2√x)","option_b":"1\/√x","option_c":"√x\/2","option_d":"2√x","option_e":"","option_f":"","bonne_reponse":"A","explication":"En réécrivant √x comme x^(1\/2), la dérivée est (1\/2)x^(-1\/2) = 1\/(2√x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26377,"question":"Le théorème fondamental de l'analyse relie dérivées et primitives.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Ce théorème stipule que l'intégrale d'une fonction est une primitive de cette fonction.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]