I assume fyx means differentiation of f with respect to y followed by differentiation with respect to x, and vice versa for fyx.

fxy = d[d(x^3+8xy)/dx]/dy

=> fxy = d(3x^2 + 8y)/dy

=> fxy = 0 + 8

=> fxy = 8

fyx = d[d(x^3+8xy)/dy]/dx

=> fyx = d[0 +...

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I assume fyx means differentiation of f with respect to y followed by differentiation with respect to x, and vice versa for fyx.

fxy = d[d(x^3+8xy)/dx]/dy

=> fxy = d(3x^2 + 8y)/dy

=> fxy = 0 + 8

=> fxy = 8

fyx = d[d(x^3+8xy)/dy]/dx

=> fyx = d[0 + 8x]/dx

=> fyx = d[8x]/dx

=> fyx = 8

**The required derivatives are fxy = 8 and fyx = 8.**