I have this question: Suppose that $f$ is a function of $t$ and $Y(t)$, while $g$ is a function of $t$ and $Z(t)$, where $dY (t) = c_1dB_1(t) + c_2dB_2(t)$, $dZ(t) = c_3dB_1(t) + c_3dB_2(t)$.
If $c_1, c_2, c_3, c_4$ are known constants and $B_1(t)$ and $B_2(t)$ are independent Brownian motions, determine the SDE for $d(fg)$.
I thought of writing out what $df$ and $dg$ would be, but I have no idea how to proceed because I'm not given what the original functions are. Can anyone help me get started on this problem?