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Math Help - directional derivative

  1. #1
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    directional derivative

    by about how much will

    g(x,y,z)=x+x*cosz-y*sinz+y

    change if the point p(x,y,z) moves from p(initial)=(2,-1,0) a distance of ds=0.2units towards the point p(final)=(0,1,2)

    i know we have to find df here

    directional derivative=df/ds

    but how to use above information to establish the result
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  2. #2
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    Re: directional derivative

    The directional derivative is \nabla f dot product a unit vector in the given direction. Since the given direction is from (2, -1, 0) to (0, 1, 2), the vector from the first to the second is <-2, 2, 2> which has length 2\sqrt{3}. Find the gradient of f at (2, -1, 0), take its dot product with <-1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3}> and, finally, multiply by the distance moved, .2.
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