I am starting with an equation:

$\displaystyle Q=\frac{at}{(1+bt^2)^3}$

to be solved for $\displaystyle \frac{dQ}{dt}$

My solutions manual has given up this hint to me:

$\displaystyle at*\frac{-6bt}{(1+bt^2)^4}+\frac{a}{(1+bt^2)^3}$

Does anyone know what rules were applied to get the equation into the form above? I looked into the quotient rule to see if I could make sense out of what happened but I don't see it yet.

Thanks in advance...