Partial Derivative of f with respect to x1

Asked Jul 07 '15 at 15:50

Active Jul 07 '15 at 15:50

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How can I calculate the partial derivative of a series like e.g. $$ a = \sum _{i=1}^n \left(2 x_i^2+z\right) $$

with respect to $x_{1}, x_{2},... x_{n}$ using Wolfram Mathematica?

I tried it with:

D[a, Subscript[x, 1]]

But it results in null, which obviously isn't true. I also tried it with:

D[a, x]

But the result of this isn't what I expected as well. I hope that anybody can help me. Thanks in advance!

asked Jul 07 '15 at 15:50

Robin

You don't have a particular value of $n$? – J. M.'s missing motivation Jul 07 '15 at 15:57
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What answer are you hoping to obtain? – bbgodfrey Jul 07 '15 at 16:16
No not really. But in my opinion it doesn't matter because all values $x_{i}$ drop out, except for $x_{1}$ in this case. – Robin Jul 07 '15 at 16:16
I hope that somebody can tell me if there is a possibility (code) to do this so that you get the right answer for the problem above. – Robin Jul 07 '15 at 16:17
1

If you are willing to set n to some large number, D[Sum[2 Subscript[x, i]^2 + z, {i, 1000000}], Subscript[x, 1]] does what you appear to wish. – bbgodfrey Jul 07 '15 at 16:21
@bb, after all the OP did say the value of $n$ doesn't matter… ;) – J. M.'s missing motivation Jul 07 '15 at 16:37
Not clean at all a = Sum[2 x[i]^2 + z, {i, n}]; deriv[i_] := D[a /. n -> i, x[i]]; deriv[3] – Dr. belisarius Jul 07 '15 at 16:40

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