Solución
$$\frac{\partial u}{\partial r} = \frac{\partial u}{\partial x}\big(\frac{\partial x}{\partial w}\frac{\partial w}{\partial r} + \frac{\partial x}{\partial t}\frac{\partial t}{\partial r}\big)\\
+ \frac{\partial u}{\partial y}\big(\frac{\partial y}{\partial w}\frac{\partial w}{\partial r} + \frac{\partial y}{\partial t}\frac{\partial t}{\partial r}\big)\\
+ \frac{\partial u}{\partial z}\big(\frac{\partial z}{\partial w}\frac{\partial w}{\partial r} + \frac{\partial z}{\partial t}\frac{\partial t}{\partial r}\big)\\$$