(Solved): Use the chain rule to find the indicated partial derivatives. \[ P=\sqrt{u^{2}+v^{2}+w^{2}}, \quad ...

Use the chain rule to find the indicated partial derivatives. \[ P=\sqrt{u^{2}+v^{2}+w^{2}}, \quad u=x e^{y}, \quad v=y e^{x}, \quad w=e^{x y} \] \( \frac{\partial P}{\partial x}, \frac{\partial P}{\partial y} \) when \( x=0, y=6 \) \[ \begin{array}{l} \frac{\partial P}{\partial x}= \\ \frac{\partial P}{\partial y}= \end{array} \] Use the chain rule to find the indicated partial derivatives. \[ w=x y+y z+z x, \quad x=r \cos (\theta), \quad y=r \sin (\theta), \quad z=r \theta \] \( \frac{\partial w}{\partial r}, \frac{\partial w}{\partial \theta} \) when \( r=2, \theta=\frac{\pi}{2} \) \[ \frac{\partial w}{\partial r}= \] \[ \frac{\partial w}{\partial \theta}= \]