Partial derivative
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 π(x, y) with respect to the choice of the quantities x and y of two different types of output. The first order conditions for this optimization are π = 0 = π. Since both partial derivatives π and π will generally themselves be functions of both arguments x and y, these two first order conditions form a system of two equations in two unknowns.
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