2.2.20 Derivatives and differentials

Problem: Find \( \frac{\partial u}{\partial x}, \frac{\partial u}{\partial y}, \frac{\partial v}{\partial x}, \frac{\partial v}{\partial y} \), if functions \( u \) and \( v \) are implicitly defined by the equalities \[ x=e^{u}+u \sin v, y=e^{u}-u \cos v . \]