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Math Help - Differentiation - Basics

  1. #1
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    Differentiation - Basics

    Hi,
    I am trying to differentiate e^{-3x}.

    I don't understand why this is the correct answer: -3e^{-3x}

    Shouldn't the answer be this: -3e^{-3x-1} ?

    My understanding of differentiation is that if y = ax^b, then y' = b \cdot ax^{b-1}
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  2. #2
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    Quote Originally Posted by sparky View Post
    Hi,
    I am trying to differentiate e^{-3x}.

    I don't understand why this is the correct answer: -3e^{-3x}

    Shouldn't the answer be this: -3e^{-3x-1} ?

    My understanding of differentiation is that if y = ax^b, then y' = b \cdot ax^{b-1}
    the power rule for derivatives only works for constant exponents

    for constant n ...

    \dfrac{d}{dx} x^n = nx^{n-1}

    for u a function of x ...

    \dfrac{d}{dx} e^u = e^u \cdot \dfrac{du}{dx}
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  3. #3
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    Quote Originally Posted by skeeter View Post
    the power rule for derivatives only works for constant exponents

    for constant n ...

    \dfrac{d}{dx} x^n = nx^{n-1}

    for u a function of x ...

    \dfrac{d}{dx} e^u = e^u \cdot \dfrac{du}{dx}
    Thanks skeeter. I understand now.
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