Given r(t) = eᵗcos(3t)i + eᵗsin(3t)j + 3eᵗk, find the derivative r'(t) and the norm of the derivative.
a) Derivative: -3eᵗcos(3t)i + 3eᵗsin(3t)j + 9eᵗk; Norm: 3eᵗ
b) Derivative: -eᵗcos(3t)i + eᵗsin(3t)j + 3eᵗk; Norm: 5eᵗ
c) Derivative: -2eᵗcos(3t)i + 2eᵗsin(3t)j + 6eᵗk; Norm: 2eᵗ
d) Derivative: -4eᵗcos(3t)i + 4eᵗsin(3t)j + 12eᵗk; Norm: 4eᵗ