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Question
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = x2 + 3xy – 7y + cos(5x)
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Solution
gx = `(del"g")/(delx) = 2x + 3y - 5 sin(5x)`
gy = `(del"g")/(dely) = 3x - 7`
gxx = `2 - 25 cos(5x)`
gyy = 0
gxy = `del/(delx) ((del"g")/(dely))`
= `del/(delx) (3x - 7)`
= 3
gyx = `del/(dely) ((del"g")/(delx))`
= `del/(dely) (2x + 3y - 5 sin(5x))`
= 3
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