How a Multivariable Function Changes with Respect to a Polar Coordinate

For a functions $f(x)$, $g(y)$ and $h(z)$, the chain rule yields $ \frac{\partial f(x)}{\partial \theta} = ( \frac{\partial f}{\partial x} ) ( \frac{\partial x}{\partial \theta} )$. $ \frac{\partial g(y)}{\partial \theta}  = (\frac{\partial g}{\partial y})…

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