Not sure what the underscore means. If it's minus, then "3x^" is incomplete.
assuming you meant
Z = 3x^2 - 2x^2y + 2y^2 + y^3 + 8
Zx = 6x - 4xy
Zy = -2x^2 + 4y + 3y^2
Zxx = 6 - 4y
Zxy = -4x
Zyy = 4 + 6y
If not that, then try using more standard notation for exponents, as I did.
Z=3x^_2x^y+2y^+y3+8
First and second order partial derivative
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