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Homework Help: Gradient vectors

  1. Feb 29, 2012 #1
    1. The problem statement, all variables and given/known data
    My textbook never explains well so I have to figure out how to do problems by reverse engineering using the solution manual. However, here is one operation that I simply cannot reverse engineer. I do not see a common pattern in these four problems. I can't figure out what operation is going on here. In the first one it looks like they're just multiplying i by x and j by y which would work but given the other 3 examples, that's not what's happening. I understand all the other steps but this is one operation that I don't understand.


    here are the full problems in case you need to see more context.

  2. jcsd
  3. Feb 29, 2012 #2


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    An appropriate response really depends on what level class you are in. One approach, which works on these problems is to remember if you have an equation ##f(x,y)=c##, which determines y implicitly as a function of x, you have the formula$$
    \frac{dy}{dx}= -\frac{f_x}{f_y}$$For example, in your problem 2 this would give$$
    \frac{dy}{dx}=-\frac x y$$Have you had any differential equations so you can solve this by separation of variables? Like I said, that's not the only way, but I don't know what you have to work with.
  4. Feb 29, 2012 #3
    I figure out the operation. You just go back to the original question and plug in the values for x and y into the original equation, simple as that.
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