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Question
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = xey + 3x2y
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Solution
`(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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