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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}) (\frac{\partial y}{\partial \theta} )$. $ \frac{\partial h(z)}{\partial \theta}  = (\frac{\partial h}{\partial z})( \frac{\partial z}{\partial \theta} )$. Suppose $F(x,y,z) \equiv f(x) g(y) h(z)$. This is…