Hello, please excuse my title if I stated the topic incorrectly.

I was given an assignment to derive the quantum mechanical operator for the z-component of the angular momentum in spherical coordinates. I have found the solution, and the derivation uses the following relationship:

$\displaystyle \frac{\partial}{\partial(y)}$ = $\displaystyle \frac{\partial(r)}{\partial(y)}$$\displaystyle \frac{\partial}{\partial(r)}$ + $\displaystyle \frac{\partial(theta)}{\partial(y)}$$\displaystyle \frac{\partial}{\partial(theta)}$ + $\displaystyle \frac{\partial(phi)}{\partial(y)}$$\displaystyle \frac{\partial}{\partial(phi)}$

I was curious if anyone might be able to tell me from what this relationship is derived from. Whenever I search "transformation to spherical coordinates" or something along those lines, I find explanations to transforming each cartesian coordinate into spherical representation, but I don't see any transformation for the partial derivative of a cartesian coordinate into spherical representation.

If anyone could help me with the "correct" term for the above relationship or the mathematical technique used to derive it, I will gladly google the details then myself.

Thank you very much!