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When you have defined the vector S=(S_x ,S_y ,S_z) and you have a function like

E_h = k1 (S_x^2 S_y^2 + S_x^2 S_z^2 + S_y^2 S_z^2) + k2 S_z - k3 S_x S_y

and you try to calculate -\frac{\partial E_h}{\partial S} what the result is?

(the S is vector)

My mind has been blocked.... help me please.