$Q=\Sigma q_i$ and its differentiation by one of its variables Suppose that $Q = q_1 + ... +q_n$. 
why is
$$\frac{dQ}{dq_i} = \Sigma_{j=1}^{n}\frac{\partial q_j}{\partial q_i}$$?
Is it related to each $q_i$ being independent to other $q_i$'s?

No, it is because differentiation is linear, ie, if $h=f+g$, then $\frac{d h}{d x} = \frac{d f}{d x} + \frac{d g}{d x}$.
