5. (8 pts) Compute the derivative of h (x) = x^3+x^2/e^3x

and simplify your answer.

h' (x) = (-3x^3 + 2x) / e^ (3x)

Step-by-step explanation:

The formula for the derivative of a quotient is ...

(u/v) ' = (vu' - uv') / v²

Using u = (x^3 + x^2) and v = e^ (3x), this becomes ...

h' (x) = (e^ (3x) (3x^2 + 2x) - (x^3 + x^2) (3) (e^ (3x)) / e^ (6x)

h' (x) = (-3x^3 + 2x) / e^ (3x)