?Prove the identity, assuming that the appropriate partial derivatives exist and are
Chapter 14, Problem 30(choose chapter or problem)
Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If \(f\) is a scalar field and \(F\), \(G\) are vector fields, then \(f F, F \cdot G\), and \(F \times G\) are defined by
\((f F)(x, y, z)=f(x, y, z) F(x, y, z)\)
\((F \cdot G)(x, y, z)=F(x, y, z) \cdot G(x, y, z)\)
\((F \times G)(x, y, z)=F(x, y, z) \times G(x, y, z)\)
\(\operatorname{div}(\nabla f \times \nabla g)=0\)
Equation Transcription:
div(∇∇) = 0
Text Transcription:
f
F
G
fF, F . G
F x G
(fF)(x, y, z) = f(x, y, z) F (x, y, z )
(F . G)(x, y, z) = F(x, y, z) . G (x, y, z )
(F x G)(x, y, z) = F(x, y, z) x G (x, y, z )
div(nabla f x nabla g) = 0
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