I need help with the explanation for this one.

If T (r)

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

This makes

$\displaystyle \frac{\partial T}{\partial x} = \frac{x}{r}\frac{dT}{dr}$

Now I need to find the second derivative:

Using operators

$\displaystyle \frac{\partial}{\partial x}(T) = \frac{x}{r}\frac{d}{dr}(T)$

For the second derivative it would become

$\displaystyle \frac{\partial}{\partial x}(\frac{dT}{dx})$ = $\displaystyle \frac{\partial}{\partial x}(\frac{x}{r}\frac{dT}{dr})$

I understand upto this point, but then I do not understand how it turns up becoming:

$\displaystyle \frac{\partial}{\partial r}(\frac{x}{r}\frac{dT}{dr})\frac{\partial r}{\partial x}$