Maîtrisez les dérivées en Terminale Mathématiques

Question 1 sur 10 10:00

[{"id":67522,"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":"5x + 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme se calcule terme par terme : f'(x) = 6x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67523,"question":"La dérivée de e^x est-elle e^x ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle est sa propre dérivée : (e^x)' = e^x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67524,"question":"Quelle est la dérivée de ln(x) pour x \u003E 0 ?","option_a":"1\/x","option_b":"x","option_c":"1","option_d":"ln(x)\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée du logarithme népérien est (ln x)' = 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67525,"question":"Si f'(x) = 0 pour tout x, que peut-on dire de f(x) ?","option_a":"f est constante","option_b":"f est croissante","option_c":"f est décroissante","option_d":"f n'est pas dérivable","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si la dérivée est nulle partout, la fonction est constante (théorème des accroissements finis).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67526,"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":"La dérivée de sin(x) est bien cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67527,"question":"Quelle est la dérivée de f(x) = (2x + 1)³ ?","option_a":"6(2x + 1)²","option_b":"3(2x + 1)²","option_c":"6x(2x + 1)²","option_d":"(2x + 1)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"On utilise 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":67528,"question":"Si f'(x) \u003E 0 sur un intervalle, alors f est croissante sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est un résultat fondamental du cours : la dérivée positive implique la croissance.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67529,"question":"Quelle est la dérivée de f(x) = x * ln(x) ?","option_a":"ln(x) + 1","option_b":"1\/ln(x)","option_c":"x + ln(x)","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"On utilise la règle du produit : f'(x) = ln(x) + x*(1\/x) = ln(x) + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67530,"question":"La dérivée de f(x) = e^(3x) est 3e^(3x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","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.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67531,"question":"Quelle est la dérivée de f(x) = 1\/x pour x ≠ 0 ?","option_a":"-1\/x²","option_b":"1\/x²","option_c":"-x","option_d":"x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 1\/x est -1\/x² (règle des puissances : x^(-1) → -x^(-2)).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]