Question #231800
Prove ∇^2{FG} = F ∇^2 F + 2∇F•∇G




1
Expert's answer
2021-09-01T18:02:24-0400

2(FG)=.(FG)=.[FG+GF]=F.G+F2G+G.F+G2F=FG+GF+2F.GNOTE:- I correct the question.∇^2(FG)\\ =∇.∇(FG)\\ =∇.[F∇G+G∇F]\\ =∇F.∇G+F∇^2G+∇G.∇F+G∇^2F\\ =F∇G+G∇F+2∇F.∇G\\ \text{NOTE:- I correct the question.}


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