+2 votes
in General by kratos

For the following functions find the gxy, gxx, gyyand gyx

g(x, y) = xey + 3x2y

1 Answer

+6 votes
by kratos
 
Best answer

$(del"g")/(del"y") = "g"_x = "e"^y + 6xy$

$(del"g")/(dely) = "g"_y = x"e"^y + 3x^2$

gxx = $(del^2"g")/(delx^2)$

= $del/(delx) [(del"g")/(delx)]$

= $del/(delx) ["e"^y + 6xy]$

= 0 + 6y

= 6y

gyy = $(del^2"g")/(dely^2)$

= $del/(dely) [(del"g")/(dely)]$

= $del/(dely) [x"e"^y + 3x^2]$

= $x"e"^y$

gxy = $(del^2"g")/(delxdely)$

= $del/(delx) [(del"g")/(dely)]$

= $del/(delx) [x"e"^y + 3x^2]$

= $"e"^y + 6x$

gyx = $(del^2"g")/(delydelx)$

= $del/(dely) [(del"g")/(delx)]$

= $del/(dely) ["e"^y + 6xy]$

= $"e"^y + 6x$

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