# Thread: derivative of fundamental matrix

1. ## derivative of fundamental matrix

if X=Q(t)X where Q(t) is an nxn matrix that depends on time t, Let φ(t) be the fundamental matrix for this system. Find the time derivative of φ
ie: d/dt φ(t)

Since we integrate component wise wouldnt we just differentiate component wise as well?

2. $\phi'=\phi Q.$