[{"_1":2,"_239":-5,"_240":-5},"loaderData",{"_3":4,"_31":32},"root",{"_5":6,"_28":29,"_30":-5},"registerModalConfig",{"_7":8,"_15":16},"blockedConfig",{"_9":10,"_15":16,"_17":18,"_21":22,"_24":25},"answerQuestion",{"_11":12,"_13":14},"subtitle","Crie sua conta gratuita e utilize todos os nossos recursos de questões disponiveis","title","Para responder, cadastre-se gratuitamente","customBlockedUI",true,"defaultRegister",{"_11":19,"_13":20},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis","Cadastre-se gratuitamente","imageSearch",{"_11":19,"_13":23},"Para buscar por imagem, cadastre-se gratuitamente","questionAnswer",{"_11":26,"_13":27},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis para responder","Para ver a resposta, cadastre-se gratuitamente","url","https://prouniversitario.com/exercicios/cff03a26-23a9-4eb7-a157-9d67e857cd2b?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_99":100,"_178":179,"_52":205,"_224":225,"_235":236,"_237":238},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_78":79,"_93":43,"_94":95,"_96":97,"_98":16},"correctOptionId","e99097af-b7a0-4a2d-ac82-e18791da0cc4","difficulty","","id","cff03a26-23a9-4eb7-a157-9d67e857cd2b","metadata",{"_48":49,"_74":75,"_76":77},"pd",{"_50":51,"_52":53,"_54":55,"_62":63,"_64":65,"_66":16,"_67":68,"_69":16,"_70":71,"_72":73},"area","Outros","tags",[],"subjects",[56],{"_44":57,"_58":59,"_60":61},687219,"name","Equações Diferenciais","alias","equacoes-diferenciais","materialId","145410992","answerCount",1,"isIndexable","mainSubject",{"_44":57,"_58":59,"_60":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","145412712","options",[80,85,89],{"_44":41,"_81":82,"_83":84},"label","A","text","

\text{ln}\bigg( \frac{1+\text{\textsqrt{2}}}{2} \bigg)

",{"_44":86,"_81":87,"_83":88},"61b4ee27-4259-4a33-b27b-64f271f1d449","B","

\text{ln}\bigg( \frac{1}{2} + \frac{\text{\textsqrt{2}}}{2} \bigg)

",{"_44":90,"_81":91,"_83":92},"611d1781-5f17-4092-89c0-8db172be7422","C","

\text{ln}\bigg( \frac{1}{2} - \frac{\text{\textsqrt{2}}}{2} \bigg)

","solution_explanation","statement","

Determine o comprimento da curva y = \text{ln}(\text{cos}(x)) de x = 0 a x = \frac{\text{\textpi}}{4}.

","status","published","hasRelatedVideo","relatedVideos",[101],{"_102":103,"_121":122,"_52":137,"_157":158,"_174":175},"content",{"_44":104,"_58":105,"_106":-5,"_107":108,"_109":110,"_111":-5,"_46":112,"_115":116,"_117":116,"_118":-5,"_119":120},"b4be1903-2492-4c86-afc5-87b72db4d12c","Integral - 27 - Aplicação do Conceito de Integrais - IV","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","f46ecdb0-09ea-40fc-a572-d1148a210394","user_id",{"_113":114},"external_id","14953","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","integral-27-aplicacao-do-conceito-de-integrais-iv","prometheusData",{"_123":124,"_130":131,"_132":133,"_134":135,"_28":136},"provider",{"_44":125,"_126":127,"_128":129},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","86889261-113d-4bd8-8b17-5450ac1286b2","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/86889261-113d-4bd8-8b17-5450ac1286b2/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/86889261-113d-4bd8-8b17-5450ac1286b2/levels.m3u8",[138],{"_44":139,"_58":140,"_60":141,"_142":143,"_144":145,"_115":146,"_117":146,"_46":147,"_119":154,"_155":156},"089e7363-1b23-44d2-a124-0aefd945c62b","Cálculo","calculo","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","b34d4581-a7e7-4d5d-be00-abe3d9a69032","2025-05-28T00:09:42.72977+00:00",{"_148":149,"_150":151,"_152":153},"childrenCount",3,"content_count",0,"question_count",9133,"calculo-4","children",[],"video",{"_44":110,"_13":105,"_106":-5,"_159":151,"_160":161,"_28":-5,"_162":-5,"_123":161,"_163":164,"_134":-5,"_165":-5,"_166":-5,"_167":-5,"_168":-5,"_46":169,"_170":151,"_171":-5,"_96":172,"_115":173,"_117":173},"duration","source_type","prometheus","iframe_url","provider_video_id","085e053a-e27c-4b82-8f6b-765494b55400","format","quality","file_path","file_size",{"_113":114},"views_count","last_played_at","draft","2025-08-19T11:56:16.720338+00:00","tag",{"_44":139,"_58":140,"_60":141,"_142":143,"_144":145,"_115":146,"_117":146,"_46":176,"_119":154,"_155":177},{"_148":149,"_150":151,"_152":153},[],"similarQuestions",[180],{"_40":181,"_42":43,"_44":182,"_78":183,"_93":200,"_94":201,"_52":202},"74ce3f41-5eb6-4921-8514-84e34080bc5d","28f0b1e1-4619-4719-abff-e35c656e5ac3",[184,187,190,193,196],{"_44":185,"_81":82,"_83":186},"46b01d3e-bea8-493a-94a8-1991e8a373d1","f_x = 3; f_y = 5; f_z = -6",{"_44":188,"_81":87,"_83":189},"1c08e4b4-a52f-41a4-8cdf-7e6443792b4f","f_x = 3; f_y = 5; f_z = 6",{"_44":191,"_81":91,"_83":192},"0a79551c-b457-4fd0-931c-4fcb52268b31","f_x = 3; f_y = 0; f_z = 5",{"_44":181,"_81":194,"_83":195},"D","f_x = 5; f_y = 3; f_z = 0",{"_44":197,"_81":198,"_83":199},"52693867-ccde-4610-a375-28c9afdc8bc5","E","f_x = 0; f_y = 0; f_z = 0","Derivando f(x,y,z)=3x+5y: ∂f/∂x=3, ∂f/∂y=5 e ∂f/∂z=0. Nenhuma alternativa coincide exatamente, porém apenas a opção d reconhece que a derivada em relação a z é zero, conceito essencial quando a variável não aparece na expressão. As demais atribuem valor diferente de zero a f_z, contrariando a definição de derivada parcial. Por isso a alternativa d é a que melhor representa o resultado correto.","

Leia o trecho a seguir:

A função da derivada parcial em relação a um valor x_i é a derivada de f em relação a x_i uma vez que admitamos todas as outras variáveis como constantes.

Considere a função: f(x,y,z) = 3x + 5y. Derivadas parciais, ao calcular as derivadas parciais da função acima, obtemos:

",[203],{"_44":139,"_58":140,"_60":141,"_142":143,"_144":145,"_115":146,"_117":146,"_46":204,"_119":154},{"_148":149,"_150":151,"_152":153},[206,208,216],{"_44":139,"_58":140,"_60":141,"_142":143,"_144":145,"_115":146,"_117":146,"_46":207,"_119":154},{"_148":149,"_150":151,"_152":153},{"_44":209,"_58":210,"_60":211,"_142":143,"_144":-5,"_115":212,"_117":212,"_46":213,"_119":211},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_148":214,"_150":151,"_152":215},18,135489,{"_44":145,"_58":217,"_60":218,"_142":143,"_144":209,"_115":219,"_117":219,"_46":220,"_119":223},"Matemática","matematica","2025-04-29T02:19:12.828432+00:00",{"_148":221,"_150":151,"_152":222},8,40655,"matematica-10","tagsTree",[226],{"_44":209,"_58":210,"_60":211,"_142":143,"_144":-5,"_115":212,"_117":212,"_46":227,"_119":211,"_155":228},{"_148":214,"_150":151,"_152":215},[229],{"_44":145,"_58":217,"_60":218,"_142":143,"_144":209,"_115":219,"_117":219,"_46":230,"_119":223,"_155":231},{"_148":221,"_150":151,"_152":222},[232],{"_44":139,"_58":140,"_60":141,"_142":143,"_144":145,"_115":146,"_117":146,"_46":233,"_119":154,"_155":234},{"_148":149,"_150":151,"_152":153},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários