Evaluate the derivative by using the appropriate product rule, where ( r₁(t) = (t², t³, t) ) and ( r₂(t) = (e³t, e²t, eᵗ) )
17. ( d/dt (r₁(t) ⋅ r₂(t)) )
18. ( d/dt (t⁴ r₁(t)) )
a) ( (6t²e³t + 3t³e²t + eᵗ) ), ( 4t³(t², t³, t) + t⁴(2t, 3t², 1) )
b) ( (4t³e³t + 3t²e²t + teᵗ) ), ( 6t²(t², t³, t) + t⁴(2t, 3t², 1) )
c) ( (6t²e³t + 6t³e²t + teᵗ) ), ( 4t³(t², t³, t) + t⁴(2t, 3t², 1) )
d) ( (4t³e³t + 6t²e²t + 2teᵗ) ), ( 6t²(t², t³, t) + t⁴(2t, 3t², 1) )