- #1
Mathman23
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Hi
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
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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