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Math Help - Directional derivative problem

  1. #1
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    Directional derivative problem

    I am suppose to find the directional derivative for the function f(x,y,z) = xy + z^2

    at the point (2,3,4) in the direction of a vector making an angle of 3pi/4 with the grad f(2,3,4)

    I have done several with this function with other specific directions but this one is confusing me.

    I know the grad is y i + x J + 2z k so at (2,3,4) this would be 3i + 2j + 8 k but where do I go from here???? Please someone nudge or push me in the correct direction!!!! Thanks
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  2. #2
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    Quote Originally Posted by Frostking View Post
    I am suppose to find the directional derivative for the function f(x,y,z) = xy + z^2

    at the point (2,3,4) in the direction of a vector making an angle of 3pi/4 with the grad f(2,3,4)

    I have done several with this function with other specific directions but this one is confusing me.

    I know the grad is y i + x J + 2z k so at (2,3,4) this would be 3i + 2j + 8 k but where do I go from here???? Please someone nudge or push me in the correct direction!!!! Thanks
    The directional derivative of f in the direction of a unit vector v is the scalar product grad(f).v. In this case, you don't know v, but you do know the formula u.v = |u||v|cos(θ) for the scalar product of two vectors, where θ is the angle between them.
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  3. #3
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    Directional derviative question

    I remember that the dot product of two vectors is equal to their magnitude's multiplied by the cos of the angle between them but since I do not have v or mag of v how does this allow me to solve this question???? I am still lost.
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  4. #4
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    Quote Originally Posted by Frostking View Post
    I remember that the dot product of two vectors is equal to their magnitude's multiplied by the cos of the angle between them but since I do not have v or mag of v how does this allow me to solve this question???? I am still lost.
    Well v is a unit vector so its magnitude is 1, and the angle between v and grad(f) is given as 3π/4 so you can work out its cosine. Problem solved!
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