I am reading the Griffiths about finding the curl of B using Biot-Savart Law. I do not understanding the step between equation (5.52) and (5.53) which finding the x components of the following:(adsbygoogle = window.adsbygoogle || []).push({});

[tex](\boldsymbol{J}\cdot\nabla^{\prime})\dfrac{\hat{\xi}}{\xi^{2}}[/tex]

where

[tex]\mathbf{\mathbf{\xi}}=\mathbf{r}-\mathbf{r}^{\prime}[/tex]

I don't know why it said using product rule 5 in his book, can get the following result:

[tex]\left(\boldsymbol{J}\cdot\nabla^{\prime}\right)\dfrac{x-x^{\prime}}{\xi^{3}}=\nabla^{\prime}\cdot\left[\dfrac{(x-x^{\prime})}{\xi^{3}}\mathbf{J}\right]-\left(\dfrac{x-x^{\prime}}{\xi^{3}}\right)\left(\nabla^{\prime}\cdot\mathbf{J}\right)[/tex]

Is there anyone know how to deduce this result?

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# About the curl of B using Biot-Savart Law

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