derivatives - partial differentiation with log function.

Can someone please help as I am stuck,

I need to show that

$$\phi=\frac{k}{2\pi}\log(x^{2}+y^{2})^{1/2}$$

satisfies Laplaces equation, however I cannot seem to differentiate this function. Note $k$ is a constant.

How do I go about partially differentiating

$$\log(\sqrt{x^{2}+y^{2}})$$

I was thinking, using chain rule, just call

$$\sqrt{x^{2}+y^{2}}=r$$

so $$\frac{1}{r}\log r+\log r$$

Any help is appreciated.