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Is curl(BF)=Bcurl(F)-Fxgrad(B) ifBandFare partially differentiable functions of x, y, and z.

Basically I would solve for the LHS and then the RHS. If I get similar answers then I have proven it, else it is not proven. However, I am stuck with the LHS. How can I perform curl(BF)? Do I:

curl(BF)=[d/dx,d/dy,d/dz]x[x^2,y^2,z^2]?

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# Prove or disprove

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