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Math Help - Derivative of e.

  1. #1
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    Derivative of e.

    Please check if i have done these correctly.

     f(x) = e^{-x^2}

     f'(x) = -2xe^{-x^2}

     f''(x)= -4x^2e^{-x^2} - 2e^{-x^2}


    Can i also write f''(x) as  -4e^{-x^2}x^2-2e^{-x^2} ??
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  2. #2
    Junior Member utopiaNow's Avatar
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    Quote Originally Posted by el123 View Post
    Please check if i have done these correctly.

     f(x) = e^{-x^2}

     f'(x) = -2xe^{-x^2}

     f''(x)= -4x^2e^{-x^2} - 2e^{-x^2}


    Can i also write f''(x) as  -4e^{-x^2}x^2-2e^{-x^2} ??
    Your f''(x) is incorrect as it should be 4x^2e^{-x^2} - 2e^{-x^2} since we started with a factor of -2x and multiplied it by -2x again when we use the chain rule to get -2x*-2x = 4x^2. And as for your re-writing of f''(x), you just moved the x^2 term around...that's not different in any meaningful way ie. just like ax^2 and x^2a are obviously the same since multiplication in \mathbb{R} is commutative. If you wish to factor f''(x) you can rewrite it as f''(x) = (4x - 2)e^{-x^2}
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