Question

how do you take the derivative of e^-3x

Answer 1

-3e^(-3x)

Answer 2

(e^x)' = e^x

Answer 3

e^-3x
Let u=-3x so that de^u=e^u(du), therefore
de^-3x=(e^-3x)d(-3x)
=(e^-3x)(-3)
=-3e^-3x

Answer 4

if \[y = e^{ax}\]\[y' =ae^{ax}\]

in your example \[a=-3\]