Editing Partial derivative (section)

===Optimization===

Partial derivatives appear in any calculus-based [[optimization]] problem with more than one choice variable. For example, in [[economics]] a firm may wish to maximize [[profit (economics)|profit]] {{math|π(''x'', ''y'')}} with respect to the choice of the quantities {{mvar|x}} and {{mvar|y}} of two different types of output. The [[first order condition]]s for this optimization are {{math|1= π<sub>''x''</sub> = 0 = π<sub>''y''</sub>}}. Since both partial derivatives {{math|π<sub>''x''</sub>}} and {{math|π<sub>''y''</sub>}} will generally themselves be functions of both arguments {{mvar|x}} and {{mvar|y}}, these two first order conditions form a [[System of equations|system of two equations in two unknowns]].