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Thread: partial derivative question

  1. #1
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    partial derivative question

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

    the function u itself is not defined.

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

    or is there a chain rule that i have to follow?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dlbsd View Post
    Say I'm given a function
    $\displaystyle u(x/r, 1/r)$

    the function u itself is not defined.

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

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

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

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