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My problem seemed very simple at glance but I keep missing one term from the answer. Any suggestions?

This is the problem:

We have $$x_i^* + \xi_i + \frac{\alpha_i}{p_i} \left[ y - \sum_{j=1}^n p_j \xi_j \right]$$ and we need to get the following $$\frac{\partial{x_i^*}}{\partial{p_i}} = -\frac{\alpha_i}{p_i} \left[\xi_i + \frac{y-\sum_{j=1}^n p_j \xi_j}{p_i}\right]$$

whilst I get the following $$ \begin{align*} \frac{\partial x_i^*}{p_i} &= -\left[y - \sum_{j=1}^n p_j \epsilon_j \right] \alpha_i p_i^{-2} (-\epsilon_i) \\ &= \frac{\epsilon_i \alpha_i}{p_i^2} \left[y - \sum_{j=1}^n p_j \epsilon_j \right] \end{align*} $$

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You took the derivative of both factors and multiplied them together, which is incorrect. You need to use the product rule.

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  • $\begingroup$ still missing the answer. $\endgroup$ – Lawrence May 23 '15 at 19:01
  • $\begingroup$ I don't doubt it; I explained why. $\endgroup$ – Greg Martin May 23 '15 at 21:12

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