Calc
posted by
C.S.
.
deriv.
h(t)=(tˆ41)ˆ3(tˆ3+1)ˆ4

Calc 
Steve
product rule and chain rule:
h = uv
h' = u'v + uv'
if u=w^n, u' = n w^(n1) w'
so, whatcha got?

Calc 
Chelle
(3t^43)^2(4t^6+4t^3)^4+(t^41)^3(12t^4+12t)^3
but i'm not sure if this is a simple as it gets.