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Math Help - Proof with the nabla operator

  1. #1
    Senior Member chella182's Avatar
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    Proof with the nabla operator

    I've tried fiddling with this but I'm getting no where.

    If f and g are two differentiable functions of x, y and z, show that \nabla(fg)=f\nabla g +g\nabla f.
    Last edited by chella182; November 15th 2009 at 07:49 AM. Reason: Editing spelling mistakes in title
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  2. #2
    Senior Member
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    Hint:

    \nabla (fg)=\frac{\partial}{\partial x}(fg)\mathbf{i}+\frac{\partial}{\partial y}(fg)\mathbf{j}+\frac{\partial}{\partial z}(fg)\mathbf{k}.

    What happens when you apply the Product Rule on each of the three components?
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  3. #3
    Senior Member chella182's Avatar
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    Ahh I see it now, cheers.
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