# What is meant by 'simultaneously computing' all partial derivatives of an arithmetic circuit?

I was reading the proof that for every arithmetic circuit of size $s$ and depth $d$ we can find a circuit $D$ of size $\mathcal{O}(s)$ and depth $\mathcal{O}(d)$. I do not understand what is meant when we say that we can construct a circuit which 'simultaneously computes' all partial derivatives of a function. Does simultaneously computing mean that there are multiple output gates or does it mean that every partial derivative is computed by some sub-circuit of of $D$.

• Several output gates. This is also apparent from the proof. – Yuval Filmus Feb 21 '16 at 6:46