Simple question about derivative and summation

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I am reading a book and I have a simple question. There is this summation:

$$ A = β\sum_\textbf{x} ||\textbf{x}||^2 r(\textbf{x})$$

after this, taking the partial derivative:

$$ \frac{\partial A }{\partial r(\textbf{x})} = β||\textbf{x}||^{2} $$ My question is: where is the summation? The result should not be $β\sum_\textbf{x} ||\textbf{x}||^2$?