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Derivatives of functions of several arguments

  • To: mathgroup at smc.vnet.net
  • Subject: [mg40379] Derivatives of functions of several arguments
  • From: cjque at umich.edu (Chris)
  • Date: Thu, 3 Apr 2003 01:43:38 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello All,

I am wondering if there is a way to take multiple derivatives of a
function with several arguments.

For example

f_0_0_0_... = f(t_1, t_2, t_3,.....) = (t_1)^5 * (t_2)^5 + (t_1)^5 *
(t_3)^5
+ (t_1)^5 * (t_4)^5 + (t_1)^5 * (t_5)^5 +  ...

f_1_0_0_...= D[f(t_1, t_2, t_3,.....), t_1])=5(t_1)^4 * (t_2)^5
+ 5(t_1)^4 * (t_3)^5 + 5(t_1)^4 * (t_4)^5 + 5(t_1)^4 * (t_5)^5 +  ...

f_1_1_0_...= D[f_1_0_0_... , t_2])=5(t_1)^4 * 5(t_2)^4

f_1_2_0_...= D[f_1_1_0_... , t_2])=5(t_1)^4 * 20(t_2)^3

f_2_2_0_...= D[f_1_2_0_... , t_1])=20(t_1)^3 * 20(t_2)^3

I would like to be able to find terms like f_2_2_0_4_0_5  , and  
f_3_0_0_0_1_5  considerinig they exsist.

Thanks a lot all,
Chris


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