Find the derivative for f(t)=ate^-kt where a and k are constants

The options I have to choose from are:
1. f'(t)=ae^-kt-atke^-kt
2. f'(t)=ae^-kt(1-tk)
3. f'(t)=e^-kt
4. 1 and 2

Use product rule
You have:
d/dx (at * e^-kt)
d/dx(at) * e^-kt + at * d/dx(e^-kt)

And chain rule
d/dx(at) * e^-kt + at * d/dx(e^-kt)
a * e^-kt + at * -ke^-kt
(ae^-kt) - (akte^-kt)

So your answer is 1)