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Math Help - Finding a Unit Vector and Direction

  1. #1
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    Finding a Unit Vector and Direction

    Hi,

    I need to find the directional derivative of a function. I know how to do this, the problem with this particular question is that the point given is

    (x,y) not equal to (0,0)

    and the direction given is "toward the origin."

    I know to find the directional derivative is simply using the dot product between the gradient of f and the unit vector, but I don't know how to determine what the unit vector here is exactly.

    Oh, the function is

    f(x,y) = ln sqrt(x^2 + y^2).

    Thanks for your help!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Finding a Unit Vector and Direction

    Quote Originally Posted by Number42 View Post
    (x,y)\neq (0,0) and the direction given is "toward the origin."
    (0,0)-(x,y)=(-x,-y) so, use u=-\dfrac{1}{\sqrt{x^2+y^2}}(x,y)
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  3. #3
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    Re: Finding a Unit Vector and Direction

    Quote Originally Posted by FernandoRevilla View Post
    (0,0)-(x,y)=(-x,-y) so, use u=-\dfrac{1}{\sqrt{x^2+y^2}}(x,y)
    ¡Gracias, mi amigo! That is exactly the breakthrough I had been looking for. I've been at this for two days now.

    Thank you once again!
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: Finding a Unit Vector and Direction

    Quote Originally Posted by Number42 View Post
    ¡Gracias, mi amigo!
    De nada, a mandar.
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