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

  • Thread starter skyturnred
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Homework Statement



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

Homework Equations





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
 

Answers and Replies

  • #2
LCKurtz
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##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.}##
 
  • #3
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OK, thanks for the help. That clears everything up for me.
 

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