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Differentiation wrt functions in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg20327] Differentiation wrt functions in Mathematica
• From: jonparker at my-deja.com
• Date: Fri, 15 Oct 1999 20:20:50 -0400
• Sender: owner-wri-mathgroup at wolfram.com

I am trying to get Mathematica 3.0 to differentiate equations
containing Sin and Cos terms, with respect to Sin[x] and Cos[x].  On
investigation of the results I find I am not getting the answer I
expect.  As a test I asked M to evaluate the following:
D[Sin[x],{Cos[x],1}]
and go the result 0.  I would have expected to get -Cos[x]/Sin[x].  If
I reformulate the expression as:
D[(1-Cos[x]^2)^.5,{Cos[x],1}]
I then get the answer I expect.  This work-around is not convenient for
the full expressions I would like to deal with.

Is there a way of reminding M the Sin=(1-Cos^2)^.5?
Thanks, Jon


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