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Given a function

z = f(x,y), where x = r * cos(\phi) and y = r * sin (\phi)

First I show that

[tex]\frac{\partial z}{\partial r} = \frac{\partial z}{\partial x} cos(\phi) + \frac{\partial z}{\partial y} sin (\phi)[/tex]

and

[tex]\frac{\partial z}{\partial \phi} = - \frac{\partial z}{\partial x} r \cdot sin(\phi) + \frac{\partial z}{\partial y} r \cdot sin(\phi)[/tex]

Finally I need to show that

[tex](\frac{\partial z}{\partial x})^2 + (\frac{\partial z}{\partial y})^2 = (\frac{\partial z}{\partial r})^2 + \frac{1}{r^2} (\frac{\partial z}{\partial \phi}) ^2[/tex]

How do I approach this part of the problem?

Sincerley

Fred

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# Homework Help: Question: Calculus

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