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Math Help - directional derivative

  1. #1
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    directional derivative

    Hello everyone,

    Could you please tell me if this is correct?

    FInd the directional derivative using f(x, y, z)=xy+z^2 as you leave the point (1,1,0) heading in the direction of the point (0,1,1)

    u=-i+0j+1k

    fx=y (0,1.1)--> 1

    fy=x --> 1

    fz=2z-->0

    u=v/magnitude= -i+1k/square root (-1^2+1^2)= -1i+k/square root (2)

    directional derivative=i+j(-1/square root of 2i+1/square root of 2k)

    (i+j)(-1/square root 2i+1/square root of 2k)

    gradient (1,0,0)=i+j+0k

    direction derivative= gradient(u)

    Thank you very much
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Chocolatelover2 View Post
    Hello everyone,

    Could you please tell me if this is correct?

    FInd the directional derivative using f(x, y, z)=xy+z^2 as you leave the point (1,1,0) heading in the direction of the point (0,1,1)

    u=-i+0j+1k

    fx=y (0,1.1)--> 1

    fy=x --> 1

    fz=2z-->0

    u=v/magnitude= -i+1k/square root (-1^2+1^2)= -1i+k/square root (2)

    directional derivative=i+j(-1/square root of 2i+1/square root of 2k)

    (i+j)(-1/square root 2i+1/square root of 2k)

    gradient (1,0,0)=i+j+0k

    direction derivative= gradient(u)

    Thank you very much
    no

    the directional derivative of a differentiable function f(x,y,z) at the point (x_0,y_0,z_0) in the direction of a unit vector \bold{u} is given by

    D_uf(x_0,y_0,z_0) = \nabla f \cdot \bold {u}
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  3. #3
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    Thank you very much

    Do you see where I went wrong? The answer is -1/square root of 2 and I got -1/square root of 2+1/square root of 2.

    Thank you
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Chocolatelover2 View Post
    Thank you very much

    Do you see where I went wrong? The answer is -1/square root of 2 and I got -1/square root of 2+1/square root of 2.

    Thank you
    i believe i see where you went wrong, but i might not be sure. what you did wasn't very coherent and confused me.

    you have \bold{u} = \left< \frac {-1}{\sqrt{2}}~,~ 0~ ,~ \frac 1{\sqrt{2}}\right>

    and \nabla f (1,1,0) = \left<  1,1,0 \right>

    now just take the dot product
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