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Use these equations to find dz/dx and dz/dy of the following

  1. Sep 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi, we are supposed to find dz/dx and dz/dy of the equation below using these:

    dz/dx=-[itex]\frac{\frac{dF}{dx}}{\frac{dF}{dz}}[/itex]

    dz/dy=-[itex]\frac{\frac{dF}{dy}}{\frac{dF}{dz}}[/itex]

    The equation is

    x[itex]^{6}[/itex]+y[itex]^{7}[/itex]+z[itex]^{5}[/itex]=2xyz

    2. Relevant equations



    3. The attempt at a solution

    I'm pretty confident I can figure out the question if someone can just help me figure out what F is in the 2 equations. I know that F usually refers to the antiderivative of a function, but in this case, there are variables and stuff on either side of the equation, so I don't even know how to find said function. It seems very similar to implicit differentiation, but the opposite. And I've never heard of implicit anti-differentiation.

    Just in case it could be useful, I found dz/dx and dz/dy via normal implicit differentiation:

    dz/dx=[itex]\frac{2yz-6x^{5}}{5z^{4}-2yx}[/itex]

    dz/dy=[itex]\frac{2xz-7y^{6}}{5z^{4}-2xy}[/itex]

    Thanks in advance for your help
     
  2. jcsd
  3. Sep 29, 2012 #2

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    ##F(x,y,z) = x^6+y^7+z^5-2xyz##. The formulas you are using apply to an equation of the form ##F(x,y,z)=\hbox{ constant.}##
     
  4. Sep 29, 2012 #3
    OK, thanks for the help. That clears everything up for me.
     
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