Lista de Exercícios Resolvida - Derivação de Funções - Matemática Básica

MINISTÉRIO DA EDUCAÇÃO UNIVERSIDADE FEDERAL DE SERGIPE CENTRO DE CIÊNCIAS EXATAS E TECNOLOGIA DEPARTAMENTO DE MATEMÁTICA Disciplina Matemática Básica 20231 Professor Diogo Gullit Segunda Lista de Exercícios Questão Derive as seguintes funções 1 fx x212x 16 fx x lnx x 2 fx xxx2 17 fx lnx 3 fx x3 2xex 18 fx ln3x 4 fx xex 19 fx lnxx2 1 5 fx xx 1x 20 fx lnlnx 6 fx ex1x 21 fx lnsin2x 7 fx sinx cosx 22 fx lnxx2 8 fx cosx1 sinx 23 fx x21 2x 9 fx x sinx1 x 24 fx xx2 1 10 fx x3 sinx 25 fx eex 11 fx ex sin2x 26 fx cosx2 12 fx 1x4 13 27 fx cossinx3 13 fx x2 1x2 1 3 28 fx x x 14 fx 2 cos3x 29 fx ex 15 fx x e1x 30 fx x52 e2x BOM TRABALHO 1 fx x21 2x x21 2x fx 2x1 2x x22 fx 2x1 2x 2x2 2 fx x xx2 x2x x x22 12x 1x2 2xx x x4 x2 2x2x 2xx x2x 2x x4 fx x2 2x2x 4x2 4x2x 2x4x fx 3x2 2x2x 2x4x fx 3 2x 2x2x 3 fx x3 2x ex x3 2xex 3x2 2 ex x3 2x ex fx ex x3 3x2 2x 2 4 fx x ex x ex 1 2x ex x ex fx ex 12x x 5 fx x x 1x x x2 1 x x2 x2 1 fx x2x2 1 x2 1 x2 x2 12 2xx2 1 2x x2 x4 2x2 1 2x3 2x 2x3 x4 2x2 1 fx 2x x4 2x2 1 6 fx ex1 x 1 x ex 1 x2 ex 1 x ex 1 x2 fx ex x 1 x2 7 fx sinx cosx sinxcosx cosx cosx sinx sinx fx cos2x sin2x 8 fx cosx1 sinx 1 sinx cosx 1 sinx2 sinx1 sinx 1 cosx cosx 1 sinx2 fx sinx sin2x cos2x cosx 1 sinx2 fx 1 sinx cosx 1 sinx2 9 fx x sinx1 x 1 x x sinx 1 x2 x cosx 1 x x sinx 1 x2 fx x cosx sinx x cosx 1 x2 10 fx x3 sinx x3 sinx 3x2 sinx x3 cosx fx x2 3 sinx x cosx 11 fx ex sin2x x sin2x ex sin2x sin2x x cos2x 2 fx ex sin2x sin2x 2 x cos2x 12 fx 1x4 33 x4 33 fx 3 x4 34 x4 3 fx 3 x4 34 4 x3 fx 12 x3 x4 34 13 fx 3 x2 1 x2 3 2 x2 1 x2 3 3 x2 1 x2 3 2 x2 1 x2 3 x2 3 x2 1 x2 32 3 x2 1 x2 3 2 2x x2 3 2x x2 1 x2 32 fx 12 x x2 32 14 fx 3 cos2x cosx fx 3 sinx cos2x 15 fx x e3x x e3x e3x x e3x 3x e3x x e3x 3x2 fx e3x 3 1x 16 fx x lnx x lnx 1 lnx x 1x 1 lnx 1 1 fx lnx 17 fx 13 lnx23 lnx 13 lnx23 1x fx 1 3 x lnx2 18 fx 13 ln3x23 ln3x 13 ln3x23 13x 3 fx 1 3 x ln3x2 19 fx 1 x x2 1 x x2 3 1 x x2 3 x2 3 x 12 x2 3 x2 3 1 x x2 3 x2 3 2x2 2 x2 3 fx 1 x x2 3 x2 3 2x2 2 x2 3 fx 1x x x2 1 fx 2x2 1 x3 x 20 fx 1lnx lnx 1 x lnx fx 1 x lnx 21 fx 1sin2x sin2x 1sin2x 2 sinx cosx fx 2 cosx sinx 22 fx 1x x2 lnx 2x x22 x 2x lnx x4 fx 1 2 lnx x3 23 fx 2x 12x 2 x2 1 2x2 2x 4x2 2x2 1 2x2 fx 2x2 2x 1 2x2 24 fx 3 x2 1 2x x x2 12 x2 1 2x2 x2 12 x2 1 x2 12 fx x2 1 x2 12 25 fx eex ex eex ex fx eex x 26 fx sinx2 x2 sinx2 2x fx 2 x sinx2 27 fx sinsinx3 sinx3 sinsinx3 cosx3 3x2 fx 3x2sinsinx3 cosx3 28 fx 12x x x x 12x x 1 12x fx 12x x 14x2 xx 29 fx ex x ex 12x fx ex 2x 30 fx x52 e2x x52 e2x 52 x32 e2x x52 e2x 2 fx 52 x32 e2x 2x52 e2x