Recall that adding the temporal derivative to the EV shifts the EV in time. 
Mathematically, this can be seen from the first order Taylor expansion:<br>
f(t+delay) ~ f(t) + df(t)/dt *delay<br>
where f(t) is the EV at time t, and df(t)/dt is the first derivative of the EV at time t.<br><br>

In practice, we are looking to fit the shifted EV to our FMRI data, Y:<br>
Y = f(t+delay)*C + error<br><br>

If we insert the first order Taylor expansion for f(t+delay), then we get:<br>
Y = f(t)*C + df(t)/dt *delay*C + error<br><br>

So, if we fit the following GLM to our FMRI data,<br>
Y = X1*A + X2*B + error<br>
where X1 is the EV and X2 is the temporal derivative of the EV, then we can see that C=A and delay*C=B. Hence, we can calculate the delay as B/A.