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Homework Help: Directional derivative tangent to a curve

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Given xz^2-yz+cos(xy)=2 which defines z implicitly in terms of x and y, find the directional derivative of z in the direction of the tangent to the curve y=x^2+2x-1 at the point (0,1) in the direction of decreasing x

    2. Relevant equations

    3. The attempt at a solution
    I'm fairly positive I just take the negative of the gradient of z multiplied by the unit vector of the tangent of the curve, all at the point. I have the gradient of z but what is the unit vector of the tangent? I think the tangent would be 2x+2 but I know it has to be divided by something to be a unit vector. This is where my notes become inconsistent and I'm not sure what to do
  2. jcsd
  3. Nov 27, 2011 #2


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    If you draw in the tangent vector to the curve, you should be able to see that [itex]\tan \theta = dy/dx[/itex], where [itex]\theta[/itex] is the angle the vector makes with the horizontal axis.
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