Answer
The derivative is $\frac{6t^2+30t+2}{(2t+5)^2}$
Work Step by Step
Using the quotient rule: $g'(t)=(\frac{u(t)}{v(t)})'=\frac{u'(t)v(t)-v'(t)u(t)}{(v(t))^2}$
$u(t)=3t^2-1 ;u'(t)=6t$
$v(t)= 2t+5;v'(t)=2$
$g'(t)=\frac{(6t)(2t+5)-(3t^2-1)(2)}{(2t+5)^2}=\frac{12t^2+30t-6t^2+2}{(2t+5)^2}=$
$\frac{6t^2+30t+2}{(2t+5)^2}$
