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Math Help - directional derivatives

  1. #1
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    directional derivatives

    f(x,y,z)=e^{x^2+y^2+z^2}; (1,10,100)

    \vec{v} = \left[\begin{array}{cc}1/\sqrt{3}\\-1/\sqrt{3}\\-1/\sqrt{3}\end{array}\right]


    \hat{v} = \left[\begin{array}{cc}1/3\sqrt{3}\\-1/3\sqrt{3}\\-1/3\sqrt{3}\end{array}\right]


    \nabla f(1,10,100) = 2e^{10101}\hat{i} + 20e^{10101}\hat{j} + 200e^{10101}\hat{k}

    \nabla f \cdot \hat{v} = \frac{-218e^{10101}}{3\sqrt{3}}

    correct?
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  2. #2
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    Re: directional derivatives

    Did you mean for \hat{v} to be the unit vector in the direction of \vec{v}? If so, you are incorrect. \vec{v} is already a unit vector.
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  3. #3
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    Re: directional derivatives

    Quote Originally Posted by HallsofIvy View Post
    Did you mean for \hat{v} to be the unit vector in the direction of \vec{v}? If so, you are incorrect. \vec{v} is already a unit vector.
    thats what I thought but the question says to find the directional derivative in the direction of a unit vector parallel to the given v
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