finding the derivative of a specific equation

Question

What is the derivative of N(t)=200te^(2-t)

Answer 1

Use the product rule and chain rule,

N(t) = 200 te^2-t

dN/dt = 200 [(1)e^2-t + te^2-t(-1)]

dN/dt = 200 (e^2-t - te^2-t) = 200 (1 - t) e^2-t