\frac{\partial r}{\partial x}=y\text{  }\frac{d}{\text{dx}}\left(f\left(\frac{x^2}{y z^3}\right) \right)=y f'\left(\frac{x^2}{y z^3}\right)\text{  }\frac{d}{\text{dx}}\left(\frac{x^2}{y z^3}\right)=y f'\left(\frac{x^2}{y z^3}\right) \frac{2x}{y z^3}=\frac{2x}{z^3} f'\left(\frac{x^2}{y z^3}\right)