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**harbottle** If f(x,y) becomes g(r,t) in a transformation from Cartesian to Polar cooardinates, show that

i) $\displaystyle \left(\frac{\partial f}{\partial x}\right)^2 + \left(\frac{\partial f}{\partial y}\right)^2= \left(\frac{\partial g}{\partial r}\right)^2 + \frac{1}{r^2}\left(\frac{\partial g}{\partial t}\right)^2$

ii) $\displaystyle \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} = \frac{\partial^2 g}{\partial r^2}+\frac{1}{r}\frac{\partial^2 g}{\partial r} + \frac{1}{r^2}\frac{\partial^2 g}{\partial t^2}$

I know the partials of x and y with respect to r and t and vice-versa; I just can't get my head around how to approach the question.

I know how to find $\displaystyle \frac{\partial f}{\partial r}$ and $\displaystyle \frac{\partial f}{\partial t}$ with the chain rule, and same for g, but not the other way round. Help!