dlnZdt=dlnXdt+dlnYdt=Z˙(t)Z(t)=X˙(t)X(t)+Y˙(t)Y(t)\frac{d \ln Z}{dt} = \frac{d \ln X}{dt} + \frac{d \ln Y}{dt} = \frac{\dot Z(t)}{Z(t)} = \frac{\dot X(t)}{X(t)} + \frac{\dot Y(t)}{Y(t)}