For a functions $f(x)$, $g(y)$ and $h(z)$, the chain rule yields $\frac{\partial f(x)}{\partial \phi} = ( \frac{\partial f}{\partial x} ) ( \frac{\partial […] Continue Reading ### How a Multivariable Function Changes with Respect to a Polar Coordinate For a functions$f(x)$,$g(y)$and$h(z)$, the chain rule yields$ \frac{\partial f(x)}{\partial \theta} = ( \frac{\partial f}{\partial x} ) ( \frac{\partial […]

First focus on the Cartesian coordinate $x$, which depends on the spherical coordinates $r,\theta,$ and $\phi$. For a function $f(x)$, the chain […]