DERIVADAS PAPRCIALES

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  CRESPIN GÁMEZ PIERO EJEMPLO: Nº 01 1.   PARA LA FUNCIÓN:  (,) = 6  +5    −10   DETERMINAR LAS PRIMERAS Y SEGUNDAS DERIVADAS PARCILAES.- Primeras derivas parciales con respecto a X e Y: -   Respecto a X:  =  = 6  +5    −10      = 12 +5  3  −0     = 12 +15     -   Respecto a Y:  =  = 6  +5    −10      = 0+5  4  −50      = 20    −50    Segundas derivadas parciales: -   Respecto a X:  →  =  = 12 +15        = 12+15  2     = 12+30   -   Respecto a y:  →  =  = 20    −50      = 20  3  −50      = 60    −200     -   Respecto a Y e X:   = =  = 12 +15        = 0 +15  4      = 60     -   Respecto a X e Y:   = =  = 20    −50      = 20  3  −0     = 60       =  EJEMPLO: Nº 02: Calcular las derivadas parciales de primer orden: A.-    (,) = 2  −3 +4   Considerando Y constante y derivando con respecto a X:  =  = 4 −3 +0    =  = 4 −3  Considerando X constante y derivando con respecto a Y:  =  = 0− 3 +8    =  = −3 +8    B.-  (,) =     +     Considerando Y constante y derivando con respecto de X:  () =    +   = 2 −     Considerando X constante y derivando con respecto a Y:  () =    +   =      +2  
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