# derive-it.com

• ## How a Multivariable Function Changes with Respect to an Azimuthal Coordinate

For a functions $f(x)$, $g(y)$ and $h(z)$, the chain rule yields $\frac{\partial f(x)}{\partial \phi} = ( \frac{\partial f}{\partial x} ) ( \frac{\partial x}{\partial \phi} )$. $\frac{\partial g(y)}{\partial \phi} = (\frac{\partial g}{\partial y}) (\frac{\partial y}{\partial \phi} )$. $\frac{\partial h(z)}{\partial \phi} = (\frac{\partial h}{\partial z})( \frac{\partial z}{\partial \phi} )$. Suppose $F(x,y,z) \equiv f(x) g(y) h(z)$. This is…

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