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21 January, 11:58

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

and simplify your answer.

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Answers (1)
  1. 21 January, 12:16
    0
    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)
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