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Find gradient at a point and the directional derivative Multivariable calculus

  1. Oct 22, 2012 #1
    Calculate gradient of f
    f(x,y)=x^3+2y^3
    at point P (1,1)
    and the directional derivative at P
    in the direction u of the given vector A -> i-j

    I tried to attempt this but i honestly don't know where to start. I began to take the partial derivatives of f. I got f'=3x^2dx+6y^2dy, however that answer doesn't seem correct to me.
     
  2. jcsd
  3. Oct 22, 2012 #2

    LCKurtz

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    What you have calculated is the total differential of f(x,y), which includes both partials ##f_x## and ##f_y##. What is the formula for the directional derivative? Show us what happens when you try to calculate it.
     
  4. Oct 24, 2012 #3
    it is the dot product of the gradient at P with a unit vector in the given direction
     
  5. Oct 24, 2012 #4

    LCKurtz

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    You ignored the part I highlighted in red.
     
  6. Oct 24, 2012 #5
    try to calculate what?don't you need to calculate the directional derivative?
     
  7. Oct 24, 2012 #6

    LCKurtz

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    Yes. You posted a question because you were apparently stuck on the problem. You have now stated that you need to take the gradient at P dotted into a unit vector. So please do it and show us what exactly you are stuck on.
     
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