Proving the Vector Calculus Identity: (1/g^2)(g∇f - f∇g)

[Rubik]

I am trying to figure out a proof for this identity

$\nabla$(f/g) = (1/g²) (g$\nabla$f - f$\nabla$g)

Any ideas?

 

[mathman]

It looks like a vector version of the derivative of a quotient. Look at each component separately.

 

[techmologist]

The quotient rule for ordinary derivatives:

(f/g)' = (gf' - fg')/g²

works for partial derivatives, too.

 

[Rubik]

Thanks so much I got it :)