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Homework Statement
Let f(x,y,z) be a function of three variables and G(x,y,z) be a vector field defined in 3D space. Prove the identity:
div(fG)= f*div(G)+G*grad(f)
Homework Equations
For F=Pi +Qj+Rk
div(F)=dF/dx + dQ/dy + dR/dz
grad(F)=dF/dx i + dQ/dy j + dR/dz k
The Attempt at a Solution
My problem starts with how do I find fG? Because I am thinking that f is a vector with i,j,k components and so is G. So fG should be the dot product of f and G, which gives a scalar, and one can't get the divergence of a scalar (Since this is an identity, I know somewhere I am missing some elementary fact)