Final answer:
The derivative of the vector function r(t) = i + 2j + e^(4t)k is r'(t) = 4e^(4t)k.
Step-by-step explanation:
To find the derivative of the vector function r(t), we need to take the derivative of each component separately. The derivative of i, j, and k with respect to t is 0 since they are constants. So the derivative of r(t) = i + 2j + e^(4t)k is r'(t) = 0i + 0j + 4e^(4t)k. Therefore, the derivative of r(t) is r'(t) = 4e^(4t)k.