TITLE: Partial derivitive of a summation.
QUESTION [0 upvotes]: I need some help taking the partial derivative of this function, if it is possible.  

Thanks!

REPLY [0 votes]: You have $\frac{\partial}{\partial x_i} \left(\lambda_1x_1+\lambda_2x_2+\lambda_3x_3+,...,+\lambda_nx_n \right)$
Note that you are taking the partial derivative with respect to a specific $x_i$ and not cycling through all the values of $i$ as you do in the summation $\sum \limits_{i=1}^n$.
For example if $i=2$ you have 
$\frac{\partial}{\partial x_2} \left(\lambda_1x_1+\lambda_2x_2+\lambda_3x_3+,...,+\lambda_nx_n \right)$
Or 
$0+\lambda_2+0+0+,...+0$
(as $x_1,x_3...x_n$ are all treated as constants)
I have assumed the $\lambda_i$ are just constants and not functions of $x_i$
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