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I'm new to Mathematica, and I'm still learning. I'm trying to code this partial differentiation. Can someone please help me find out where I coded wrong? I've attached a hand-written solution below.

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    $\begingroup$ Please post your code, not images. Thanks. $\endgroup$ – Rohit Namjoshi Apr 19 '20 at 0:30
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D[x1Com,x[1,i]] will give zero, since there is no x[1,i] any more in x1Com. There is only x[1,1] and x[1,2] and so on.

One way could be

ClearAll[x1Com, x, m];
x1Com = HoldForm@(Sum[(m[1, i]*x[1, i]), {i, 1, 6}]/Sum[m[1, i], {i, 1, 6}])

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Now make a function to differentiate w.r.t. to specific x[1,i]

diff[x1Com_, x_] := D[ReleaseHold@x1Com, x];

Now use it

diff[x1Com, x[1, 1]]

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diff[x1Com, x[1, 2]]

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And so on.

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