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

[skyturnred]

Homework Statement

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

dz/dx=-$\frac{\frac{dF}{dx}}{\frac{dF}{dz}}$

dz/dy=-$\frac{\frac{dF}{dy}}{\frac{dF}{dz}}$

The equation is

x$^{6}$+y$^{7}$+z$^{5}$=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=$\frac{2yz-6x^{5}}{5z^{4}-2yx}$

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

Thanks in advance for your help

 

[LCKurtz]

$F(x,y,z) = x^6+y^7+z^5-2xyz$. The formulas you are using apply to an equation of the form $F(x,y,z)=\hbox{ constant.}$

 

[skyturnred]

OK, thanks for the help. That clears everything up for me.