Question about asymptotic stability in ordinary differential equation

Question about asymptotic stability in ordinary differential equation

I am studying for a exam in ordinary differential equations and got stuck
on this question:
"Show that if the origin is asymptotically stable for one of the following
systems of ode's then the same holds for the other one
1) x'=f(x)
2) x'=f(x)h(x)
f is C^1(R^n,R^m),h(0) = 0 and h is C^1(R^n,R) , h(0)>0."
I have no idea where to start on this one. Im also confused about the "
h(0) = 0 and h is C^1(R^n,R) , h(0)>0." part. Can't make sense of it.
Thanks in advance!
Best regards, Per