find the derivative of the function y=(x^2)(e^-3x)

Question

find the derivative of the function

 

y=(x^2)(e^-3x)

Answer 1

in this problem, let u = x² and let v = e^-3x so that y = uv and you can use the product rule: y' = u'v + uv'

 

u' = 2x   v' = -3e^-3x

 

Now just substitute all four of the parts into the formula on first line above, and simplify (by factoring).