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I Question about Cross Product and Derivative

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  1. Feb 4, 2017 #1
    Hi everyone,

    Given a vector-valued function ##\vec{A}##, how do I show that:

    $$\vec{\nabla} \times \left(\frac{\partial \vec{A}}{\partial x}\right) = \frac{\partial}{\partial x}(\vec{\nabla} \times \vec{A})$$

    In other words, are the cross product and derivative commutative w/ each other? I have an intuition that this is true, but I would like to know a good way to show this.

    Thank you very much.
     
  2. jcsd
  3. Feb 4, 2017 #2

    pasmith

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    Homework Helper

    If in doubt, write it out component by component and check.

    Assuming the components of [itex]\mathbf{A}[/itex] are sufficiently smooth, partial derivative operators will commute.
     
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