Computing divergence of r̂/r² in Cartesian coordinates

[shaun_chou]

I know that this question was posted before but I just couldn't get it using another way around. So your comments are highly appreciated. In the textbook, $$\nabla\bullet\left(\widehat{r}/r^{2}\right)=4\pi\delta^{3}\left(r\right)$$. But when I want to calculate the divergence using Catesian coordinates then it comes to calculate $${\frac{\partial}{\partial\,x} x/(x^{2}+y^{2}+z^{2})^{3/2}}$$ but I can't get the results of "zero" as it claimed. Where did I go wrong?

 

[Bob_for_short]

You have to add three derivatives to get zero, not only x-component. You will obtain 1/r³ - 1/r³.