http://www.physics.usu.edu/Wheeler/QuantumMechanics/QMOrbitalAngularMomentum.pdf
Unfortunately, this is the first time I've come across a conversion to spherical coordinates and I'm pretty lost.
The set of equation at the bottom of page 2 is confusing me. Actually obtaining it via the chain rule is simple.
But how do I use it ? Specifically (and this is my major issue) how is $\frac{\partial r}{\partial x}=\frac{x}{r}$ ?
$$\frac{\partial r}{\partial x}=\frac{\partial}{\partial x}\sqrt{x^2+y^2+z^2}=\frac{2x}{2\sqrt{x^2+y^2+z^2}}=\frac{x}{r}$$