Question

If f(t)=(t^2+6t+2)(3t^2+3)

then f'(t)=_____?

and f'(3)=______?

Answer 1

application of the product rule
f'(x) = (t^2+6t+2)(6t) + (3t^2+3)(2t+6)

expand the above, collect like terms and simplify

for f'(3) sub t=3 into the above result