Given f(t)=∫1t2w3+1dwf(t) = \int_1^{t^2} \sqrt{w^3+1} dwf(t)=∫1t2w3+1dw, find the derivative f′(t)f'(t)f′(t).
t6+1\sqrt{t^6+1}t6+1
2tt6+12t\sqrt{t^6+1}2tt6+1
t2+1\sqrt{t^2+1}t2+1
t2t6+1t^2\sqrt{t^6+1}t2t6+1