Dérivées et Primitives : Testez vos connaissances en Terminale Maths !

Question 1 sur 10 10:00

[{"id":66232,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66233,"question":"La fonction f(x) = e^(2x) a pour dérivée f'(x) = 2e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai. La dérivée de e^(u(x)) est u'(x)e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66234,"question":"Quelle est la primitive de la fonction 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 d'une fonction 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":66235,"question":"La primitive 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 vrai. La primitive de 1\/x est ln|x| + C, définie pour x ≠ 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66236,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 1) ?","option_a":"1\/(3x + 1)","option_b":"3\/(3x + 1)","option_c":"1\/(x + 1)","option_d":"3\/(x + 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. Ainsi, f'(x) = 3\/(3x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66237,"question":"La primitive 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 vrai. La dérivée de sin(x) est cos(x), donc la primitive de cos(x) est sin(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66238,"question":"Quelle est la dérivée de la fonction f(x) = (x² + 1)³ ?","option_a":"3(x² + 1)²","option_b":"6x(x² + 1)²","option_c":"3x(x² + 1)²","option_d":"6x²(x² + 1)²","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est un cas de dérivation d'une fonction composée. On applique la formule (u^n)' = n*u'*u^(n-1). Ici, u = x² + 1, donc u' = 2x. Ainsi, f'(x) = 3*(2x)*(x² + 1)² = 6x(x² + 1)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66239,"question":"La primitive 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 vrai. La dérivée de -e^(-x) est e^(-x), donc la primitive de e^(-x) est -e^(-x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66240,"question":"Quelle est la dérivée de la fonction f(x) = √(x² + 4) ?","option_a":"x\/√(x² + 4)","option_b":"2x\/√(x² + 4)","option_c":"(x² + 4)^(-1\/2)","option_d":"x\/√(x² + 4) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est un cas de dérivation d'une fonction composée. On applique la formule (√u)' = u'\/(2√u). Ici, u = x² + 4, donc u' = 2x. Ainsi, f'(x) = 2x\/(2√(x² + 4)) = x\/√(x² + 4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66241,"question":"La primitive de f(x) = 1\/(1 + x²) est arctan(x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai. La dérivée de arctan(x) est 1\/(1 + x²), donc la primitive de 1\/(1 + x²) est arctan(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]