I've come across a very ambiguous statement in my notes on implicit functions (part of the partial derivatives part of the course). I'll write out the preceding explanation but the problematic line is marked by *(adsbygoogle = window.adsbygoogle || []).push({});

"Sometimes we can define a function z=z(x, y) only in implicit form, i.e. through an equation F(x, y, z) = 0.

It is not always possible to solve this equation for z and obtain the function z=f(x,y).

In order to calculate the derivatives of a function defined implicitly we note that from the above equation it follows that:

* [tex]\delta[/tex]F=0 [tex]\Rightarrow[/tex] [tex]\delta[/tex]F = F_{x}[tex]\delta[/tex]x + F_{y}[tex]\delta[/tex]y + F_{z}[tex]\delta[/tex]z = 0.

Or by taking differentials,

F_{x}dx + F_{y}dy + F_{z}dz = 0"

My main problem is understanding how [tex]\delta[/tex]x can stand on its own (above used as a factor). Is it just the same as ∆x, i.e. a change in x and not a derivative?

Also, how the [tex]\delta[/tex] expressions change to d expressions in the second line is unclear to me...

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# Meaning of delta?

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