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Partial derivatives and implicit inversion?

• To: mathgroup at smc.vnet.net
• Subject: [mg33006] Partial derivatives and implicit inversion?
• From: jflanigan at netzero.net (jose flanigan)
• Date: Mon, 25 Feb 2002 01:31:24 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

I have two functions in polar coordinates.

f[r,t],g[r,t]

and I want to find dg/df ( where "d" indicates
PARTIAL differentiation).

The problem is that I cannot explicitly express
r,t in terms of f,g. so, I want something like

dg/df = dg/dr * dr/df + dg/dt * dt/df

but I don't have dr/df or dt/df. I don't feel safe computing
df/dt and then inverting it. I think I'm missing a step somewhere.

Any help or references appreciated.

Thanks in advance.