First, we need to find the partial derivatives of the production function with respect to x and y.
$f_x(x, y) = \frac{\partial f(x, y)}{\partial x} = 100 \cdot 0.75 x^{0.75 - 1} y^{0.25} = 75 x^{-0.25} y^{0.25}$
$f_y(x, y) = \frac{\partial f(x, y)}{\partial y} =
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