1. partial derivative question

Say I'm given a function
$u(x/r, 1/r)$

the function u itself is not defined.

when i take a partial derivative with respect to x, do i just write it as
$u_x(x/r, 1/r)$

or is there a chain rule that i have to follow?

2. Originally Posted by dlbsd
Say I'm given a function
$u(x/r, 1/r)$

the function u itself is not defined.

when i take a partial derivative with respect to x, do i just write it as
$u_x(x/r, 1/r)$

or is there a chain rule that i have to follow?
indeed there is a chain rule.

let $s = \frac xr$ and $t = \frac 1r$, then you want $\frac {\partial}{\partial x} u(s,t)$.

by the chain rule, $\frac {\partial u}{\partial x} = \frac {\partial u}{\partial s} \cdot \frac {\partial s}{\partial x} + \frac {\partial u}{\partial t} \cdot \frac {\partial t}{\partial x}$