Proving/Disproving Curl(BF)=Bcurl(F)-Fxgrad(B)

[caseyjay]

Hi all,

Is curl(BF)=Bcurl(F)-Fxgrad(B) if B and F are 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]?

 

[Office_Shredder]

F has to be a vector function, and B has to be a scalar function (otherwise grad(B) would be meaningless! So would Bcurl(F)!). So if F has components F_i, then BF has components BF_i