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Re: Differentiation wrt functions in Mathematica

  • To: mathgroup at
  • Subject: [mg20361] Re: [mg20327] Differentiation wrt functions in Mathematica
  • From: "Andrzej Kozlowski" <andrzej at>
  • Date: Sun, 17 Oct 1999 03:01:49 -0400
  • Sender: owner-wri-mathgroup at

Mathematica's D[f,x] ignores any implicit relationships between f and x. You
can get what you want by using the total derivative Dt:

Dt[Sin[x], Cos[x]] /. Dt[x, f_] -> 1/Dt[f, x]

This is better than what you get by using your "reformulation":

D[(1 - Cos[x]^2)^(1/2), {Cos[x], 1}] // Simplify
  Sqrt[Sin[x] ]

The reason of course is that it is not true that Sin[x] is always (1 -
Cos[x]^2)^(1/2), sometimes it is -(1 - Cos[x]^2)^(1/2).
Andrzej Kozlowski
Toyama International University

>From: jonparker at
>To: mathgroup at
>Subject: [mg20361] [mg20327] Differentiation wrt functions in Mathematica
>Date: Sat, Oct 16, 1999, 9:20

> 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
> Sent via
> Before you buy.

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