?Prove the following identity:\(\nabla(F \cdot G)=(F \cdot \nabla) G+(G \cdot \nabla)

Chapter 16, Problem 5

(choose chapter or problem)

Prove the following identity:

$\nabla(F \cdot G)=(F \cdot \nabla) G+(G \cdot \nabla) F+F \times \operatorname{curl} G+G \times \operatorname{curl} F$

Equation Transcription:

∇ $(F\bullet{}G)=(F\bullet{}$ ∇ $)G+(G\bullet{}$ ∇ $)F+F\ \times{}\ curl\ G+G\ \times{}\ curl\ F$

Text Transcription:

nabla (F . G)=(F . nabla)G+ (G . nabla)F + F x curl G + G x curl F

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