Differentiation Problem -

**tim85ruhruniv** · Jun18-09, 01:34 PM

I was working on some of my own equations and today i ended up with this differentiation thinghy, I never expected this in my equation but it just turned up :( so if there's anybody out there who loves to solve math please give this a try :)

maybe its too simple :) ... i am just having doubts about the order of the operations and their influences...

me too will try solving it in the mean time...

$LaTeX Code: \\frac{d}{d\\theta}\\left\\{ \\nabla\\left(\\underset{k}{\\sum}\\left[n_{k}+\\theta n_{j}^{\\star}\\right]z_{k}^{2}\\right)^{\\frac{1}{2}}\\right\\} =?$

$LaTeX Code: \\[ n_{k},n_{j}^{\\star}\\]$ are independent of $LaTeX Code: \\theta$
$LaTeX Code: \\[ n_{k},n_{j}^{\\star}\\]$ depend on x,y,z (grad) (Actually these variables are concentrations defined at each point in our domain)
$LaTeX Code: \\[ z_{k}^{2}\\]$ is a constant (actually the valence of the kth chemical species)

$LaTeX Code: \\theta$ is also independent of the geometry (x,y,z)... i call it the ALIEN variable :) because afterwards i have to kill it by setting it to zero, that is after differentiation...

Thanks a lot,

Tim

**tim85ruhruniv** · Jun18-09, 01:59 PM

$LaTeX Code: \\[ =-\\frac{1}{2}\\left(\\underset{k}{\\sum}\\left[n_{k}+\\theta n_{j}^{\\star}\\right]z_{k}^{2}\\right)^{-\\frac{3}{2}}n_{j}^{\\star}\\nabla\\underset{k}{\\sum}\\ left[n_{k}+\\theta n_{j}^{\\star}\\right]z_{k}^{2}\\] \\[ +\\frac{1}{2}\\underset{k}{\\sum}\\left[n_{k}+\\theta n_{j}^{\\star}\\right]z_{k}^{2}\\nabla n_{j}^{\\star}\\]$

can someone confirm :)

Thanks a lot ....