Question about derivatives
- To: mathgroup at smc.vnet.net
- Subject: [mg51384] Question about derivatives
- From: "Ben Whale" <ben.whale at anu.edu.au>
- Date: Fri, 15 Oct 2004 02:48:03 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi, I want to treat a function abstractly, I know that it is a function of n variables. I wish to take its derivative after addition or multiplication with another function. However Derivative does not return what I expect. Derivative[0,1][f+g] gives (f+g)^(0,1) instead of f^(0,1)+g^(0,1) and Derivative[0,1][fg] gives (fg)^(0,1) instead of f^(0,1)g+g^(0,1)f. Now perhaps I'm going about my problem in the wrong way, if I am please tell me. I also have some other questions about Derivative, Derivative[0,1][Composition[f,g]] gives f^(0,1)(g)g^(0,1), the correct result, why does Derivative know the chain rule and not the product rule? Also, in order to get the correct behaviour for Derivative[0,1][f+g], I can use the Map function, that is Map[Derivative[0,1],f+g] returns f^(0,1) +g^(0,1). Which is fine except that if I have the function 1+f and apply the same command to it I get 0& + f^(0,1), instead of f^(0,1). Clearly this is because of the presence of the command Function[0], however I have been unable to find a function that fixes this problem. In essence I want to do vector operations of the ring of functions, but find that doing this in Mathematica is hard. How can I do this easily? Surely someone else has figured out a convenient way of do this. Thanks, Ben