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Math Help - Directional Derivative

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    Directional Derivative

    Find the directional derivative of f(x,y,z)=xy+z^2 at the point (1,2,3) in the direction of a vector making an angel of pi/4 with gradf(1,2,3).
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Directional Derivative

    Quote Originally Posted by mgwalker View Post
    Find the directional derivative of f(x,y,z)=xy+z^2 at the point (1,2,3) in the direction of a vector making an angel of pi/4 with gradf(1,2,3).
    As f is differentiable at (1,2,3) the directional derivative in the direction of u\;(||u||=1) is

    (\nabla f)(1,2,3)\cdot u=|| (\nabla f)(1,2,3) ||\;||u||\cos (\pi/4)=\ldots
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