\text { Let } \int(x, y) \text { be a } C^{2}-\text { function and } g(r, \theta):=\int(r \cos \theta, r \sin \theta) \text {. Show that } \frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}=\frac{\partial^{2} g}{\partial r^{2}}+\frac{1}{r} \frac{\partial g}{\partial r}+\frac{1}{r^{2}} \frac{\partial^{2} g}{\partial \theta^{2}}

Fig: 1

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