# derive-it.com

• ## Investigating the Meaning of a Function to the Right of the Del Operator

Let $F(x,y,z) \equiv f(x) g(y) h(z)$. In this previous post, $\vec{\nabla}F(x,y,z)$ was written in terms of spherical coordinates and unit vectors for a spherical coordinate system. The corresponding equation was found to be $\vec{\nabla}F(x,y,z) = \vec{e}_r \frac{\partial F(x,y,z) }{\partial r} + \vec{e}_\theta \frac{1}{r} \frac{\partial F(x,y,z) }{\partial \theta} + \vec{e}_\phi \frac{1}{r\sin\theta} \frac{\partial F(x,y,z) }{\partial \phi}$. This is (6)…

• ## How a Multivariable Function Changes with Respect to the Cartesian Coordinates

Suppose $F(x,y,z) \equiv f(x) g(y) h(z)$. This post shows how to calculate a partial derivative of a multivariable function $F(x,y,z)$ with respect to each Cartesian coordinates. The resulting expressions are in spherical coordinates. In previous posts (see references , , and ), the following equations were written: \$ \frac{\partial }{\partial r} F(x,y,z) = \bigg( ( \frac{\partial x}{\partial r}…