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I am trying to take partial derivative of sum: $$Cv_m=\sum_{i=1}^{Ns}Cv_i \frac{\rho_i}{\rho_m},$$ where $Cv_i$ are constants. I want to take derivative $$\partial{Cv_m}/\partial\rho_i=Cv_i /\rho_m$$

D[Sum[Subscript[Cv, i]*Subscript[rhoY, i]/rhom, {i, 1, 
    Ns}], Subscript[rhoY, i]]

I expected $Cv_i/\rho_m$, but it gives me $\sum_{i=1}^{Ns}Cv_i/\rho_m$

How get rid of sum symbol?

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  • $\begingroup$ Try avoiding subscripts for a start, see if it simplifies things at all. $\endgroup$ – MarcoB Jun 3 '18 at 17:46
  • $\begingroup$ I chose it because Wolfram "considers" that it is an argument and it gives me 0. For example: Dt[rhoY[i]/rhom] gives me $-\frac{\text{rhoY}(i) Dt[\text{rhom}]}{\text{rhom}^2}$ instead $\frac{Dt[\text{rhoY[i]}]}{rhom}-\frac{\text{rhoY}(i) Dt[\text{rhom}]}{\text{rhom}^2}$ $\endgroup$ – Евгений Львович Шараборин Jun 4 '18 at 6:44
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Have a closer look, the output of the following contains a KroneckerDelta:

a = D[Sum[Cv[i]*ρ[i]/ρ[m], {i, 1, Ns}], ρ[j]]

$$\sum _{i=1}^{\text{Ns}} \frac{\text{Cv}(i) \delta _{i,j}}{\rho (m)}$$

so the result is correct.

You can get rid of the sum with

Assuming[j \[Element] Integers && 1 <= j <= Ns, Simplify[a]]

$$\frac{\text{Cv}(j)}{\rho (m)}$$

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