Question

d/dxdy(x^3+y^3-3x-12y

Answer 1

Do you mean \[d^2/dxdy (x^3+y^3-3x-12y)\]? In that case we first differentiate with respect to y, and then w.r.t x. So \[d^2/dxdy(x^3 + y^3 -3x -12y) = d/dx[d/dy(x^3 + y^3 -3x -12 y)] = d/dx (3y^2 -12) = 0\]

Answer 2

The answer is "Zero", in second derivative when one for x and one for y, if the function do not have a sentence that contains both x and y, the derivative of x and y with be zero