7. If f(x) = ae^-ax for a > 0, then f'(x) =

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7. If f(x) = ae^-ax for a > 0, then f'(x) =

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Minh Khuê 5 years 2021-07-31T17:10:36+00:00 1 Answers 303 views 0

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  1. King
    0
    2021-07-31T17:11:39+00:00
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    Answer:

    f'(x)=-a^2e^{-ax}

    General Formulas and Concepts:

    Calculus

    • Chain Rule: \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)
    • Derivative: \frac{d}{dx} [e^u]=e^u \cdot u'

    Step-by-step explanation:

    Step 1: Define

    f(x)=ae^{-ax}

    Step 2: Find Derivative

    1. Derivative eˣ [Chain Rule]:                    f'(x)=ae^{-ax} \cdot -a
    2. Condense/Simplify:                               f'(x)=-a^2e^{-ax}

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