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Math Help - Directional Derivative

  1. #1
    Junior Member
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    Directional Derivative

    I've been at this problem for a while!
    Find the directional derivative of the given function at the point (3,-1) in the direction theta=(pi)/4.

    f(x,y)=4x+xy^2-5y

    fx=4+y^2
    fy=2xy-5

    applying ponts:
    fx=4+(-1)^2=5
    fy=2(3)(-1)-5=-11

    <5, -11>

    But how would I find my unit vector in the direction of theta=pi/4?
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  2. #2
    MHF Contributor

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    Quote Originally Posted by latavee View Post
    I've been at this problem for a while!
    Find the directional derivative of the given function at the point (3,-1) in the direction theta=(pi)/4.

    f(x,y)=4x+xy^2-5y

    fx=4+y^2
    fy=2xy-5

    applying ponts:
    fx=4+(-1)^2=5
    fy=2(3)(-1)-5=-11

    <5, -11>

    But how would I find my unit vector in the direction of theta=pi/4?
    The unit vector in direction \theta is \left<cos(\theta), sin(\theta)\right>.

    The directional derivative of f in the direction of unit vector \vec{v} is \nabla f\cdot\vec{v}.
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