Question

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

Answer 1

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

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)