A current textbook I'm reading has the following example of how to take derivatives of summations $$\frac{d}{dt}\sqrt{\sum_jA_jB_j} = \frac{\sum_k\dot{A}_kB_k + A_k\dot{B}_k}{2\sqrt{\sum_jA_jB_j}}$$ where the overdots indicate time derivatives.
Why do we need to change the dummy index from $j$ to $k$ on the numerator? Shouldn't it not matter since both $j$ and $k$ run from 1 to $n$?
Thank you.