Suppose $x,y,$ and $z$ are positive functions of $t.$ If $z^2=x^2+y^2,d\frac{x}{d}t=1,$ and $d\frac{y}{d}t=3,$ find $d\frac{z}{d}t$ when $x=8$ and $y=15.$

$\frac{dz}{dt}=$