consider the level curve x3y3z36xyz72 Near the point 123 the

consider the level curve x^3+y^3+z^3+6xyz=72. Near the point (1,2,3) the variable z is implictly a function of x and y, say z=f(x,y). Use the implict function theorem to find partial df/dx(1,2)

x^3+y^3+z^3+6xyz=72 partially differentiating both sides w.r.t x 3x^2 + 0 + 3z^2 df/dx + 6yz + 6xy df/dx =0 put x=1, y=2, z=3 3 + 27 df/dx+ 36 + 12 df/dx =0 df/dx = -1