[{"_1":2,"_245":-5,"_246":-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/a80d42eb-180f-41a3-a13d-1ce18f9f6637?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_107":108,"_186":187,"_51":211,"_230":231,"_241":242,"_243":244},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_77":78,"_101":41,"_102":103,"_104":105,"_106":16},"correctOptionId","","difficulty","id","a80d42eb-180f-41a3-a13d-1ce18f9f6637","metadata",{"_47":48,"_73":74,"_75":76},"pd",{"_49":50,"_51":52,"_53":54,"_61":62,"_63":64,"_65":16,"_66":67,"_68":36,"_69":70,"_71":72},"area","Outros","tags",[],"subjects",[55],{"_43":56,"_57":58,"_59":60},37020404,"name","Equações Diferenciais Ordinárias","alias","equacoes-diferenciais-ordinarias","materialId","115138714","answerCount",1,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","174079046","options",[79,85,89,93,97],{"_43":80,"_81":82,"_83":84},"bb86e7a0-ed02-4ad1-a4d9-0436d31142f1","label","A","text","y = c_1 x",{"_43":86,"_81":87,"_83":88},"e1b3d49b-8114-4998-bd0d-588547d02213","B","3x + 4y = c_1",{"_43":90,"_81":91,"_83":92},"1d0a7f9d-c2d6-4c0a-9aff-38aeb3a4e150","C","c_1 x^{2} + y^{2} = 1",{"_43":94,"_81":95,"_83":96},"34560307-5ea0-49ad-8062-24d17d74f88c","D","y = e^{(c_1 x)}",{"_43":98,"_81":99,"_83":100},"6d4cac04-929f-465f-bcec-f0ef127a7c70","E","y = \\frac{1}{\\ln(c_1 x)}","solution_explanation","statement","

Encontre as trajetórias ortogonais da famı́lia de curvas dada.

","status","pending_classification","hasRelatedVideo","relatedVideos",[109],{"_110":111,"_129":130,"_51":145,"_165":166,"_182":183},"content",{"_43":112,"_57":113,"_114":-5,"_115":116,"_117":118,"_119":-5,"_45":120,"_123":124,"_125":124,"_126":-5,"_127":128},"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",{"_121":122},"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",{"_131":132,"_138":139,"_140":141,"_142":143,"_28":144},"provider",{"_43":133,"_134":135,"_136":137},"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",[146],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":155,"_127":162,"_163":164},"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",{"_156":157,"_158":159,"_160":161},"childrenCount",3,"content_count",0,"question_count",9133,"calculo-4","children",[],"video",{"_43":118,"_13":113,"_114":-5,"_167":159,"_168":169,"_28":-5,"_170":-5,"_131":169,"_171":172,"_142":-5,"_173":-5,"_174":-5,"_175":-5,"_176":-5,"_45":177,"_178":159,"_179":-5,"_104":180,"_123":181,"_125":181},"duration","source_type","prometheus","iframe_url","provider_video_id","085e053a-e27c-4b82-8f6b-765494b55400","format","quality","file_path","file_size",{"_121":122},"views_count","last_played_at","draft","2025-08-19T11:56:16.720338+00:00","tag",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":184,"_127":162,"_163":185},{"_156":157,"_158":159,"_160":161},[],"similarQuestions",[188],{"_40":189,"_42":41,"_43":190,"_77":191,"_101":206,"_102":207,"_51":208},"74ce3f41-5eb6-4921-8514-84e34080bc5d","28f0b1e1-4619-4719-abff-e35c656e5ac3",[192,195,198,201,203],{"_43":193,"_81":82,"_83":194},"46b01d3e-bea8-493a-94a8-1991e8a373d1","f_x = 3; f_y = 5; f_z = -6",{"_43":196,"_81":87,"_83":197},"1c08e4b4-a52f-41a4-8cdf-7e6443792b4f","f_x = 3; f_y = 5; f_z = 6",{"_43":199,"_81":91,"_83":200},"0a79551c-b457-4fd0-931c-4fcb52268b31","f_x = 3; f_y = 0; f_z = 5",{"_43":189,"_81":95,"_83":202},"f_x = 5; f_y = 3; f_z = 0",{"_43":204,"_81":99,"_83":205},"52693867-ccde-4610-a375-28c9afdc8bc5","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:

",[209],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":210,"_127":162},{"_156":157,"_158":159,"_160":161},[212,214,222],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":213,"_127":162},{"_156":157,"_158":159,"_160":161},{"_43":215,"_57":216,"_59":217,"_150":151,"_152":-5,"_123":218,"_125":218,"_45":219,"_127":217},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_156":220,"_158":159,"_160":221},18,135489,{"_43":153,"_57":223,"_59":224,"_150":151,"_152":215,"_123":225,"_125":225,"_45":226,"_127":229},"Matemática","matematica","2025-04-29T02:19:12.828432+00:00",{"_156":227,"_158":159,"_160":228},8,40655,"matematica-10","tagsTree",[232],{"_43":215,"_57":216,"_59":217,"_150":151,"_152":-5,"_123":218,"_125":218,"_45":233,"_127":217,"_163":234},{"_156":220,"_158":159,"_160":221},[235],{"_43":153,"_57":223,"_59":224,"_150":151,"_152":215,"_123":225,"_125":225,"_45":236,"_127":229,"_163":237},{"_156":227,"_158":159,"_160":228},[238],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":239,"_127":162,"_163":240},{"_156":157,"_158":159,"_160":161},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários