GUIA 4.pdf - UNIVERSIDAD TECNOLOGICA DE EL SALVADOR ASIGNATURA MATEMATICA IV ESCUELA DE CIENCIAS APLICADAS “ ING JULIO CESAR ORANTES” GUIA Nº 4

GUIA 4.pdf - UNIVERSIDAD TECNOLOGICA DE EL SALVADOR...

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UNIVERSIDAD TECNOLOGICA DE EL SALVADOR ASIGNATURA: MATEMATICA IV, ESCUELA DE CIENCIAS APLICADAS “ ING. JULIO CESAR ORANTES” , GUIA Nº 4. CATEDRA DE CIENCIAS Y MATEMATICA. Aplicaciones de las Derivadas Parciales. 1. Encuentre el diferencial total para cada una de las siguientes funciones: a) 3 2 4y 3xy 5x z R// dy 12y 3x dx 3y 10x dz 2 b) ycosx cosy x z R// dy cosx y sen x dx senx y cosy dz c) 2 y 2 x e z R// dy 2ye dx 2xe dz 2 y 2 x 2 y 2 x d) 2 2 y x x z R// dy y x 2xy dx y x x y dz 2 2 2 2 2 2 2 e) y x ylnx z R// dy y x lnx dx y 1 x y dz 2
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f) 2 2 2 z y ln x w R// dz z y z 2x dy z y y 2x dx z y 2xln dw 2 2 2 2 2 2 2 2 g) x sen y 2z w 3 R// dx senx y 6z dy senx 2z dx ycosx 2z dw 2 3 3 h) yz sen z y x w 2 2 R// ? 2. Usando diferenciales, encontrar la variación aproximada de la función dada, cuando las variables experimentan los cambios que se indican. a) 3y 2xy x y x, f 2 , cuando y x , cambia de 3 , 2 a 2 . 3 , 1 . 2 R// -0.4 b) 2 2 y x y x, f , cuando y x ,
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  • Fall '16
  • alej
  • Derivada, Regla de la cadena, Cateto, Triángulo rectángulo, Pulgada

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