This is done by taking the derivative of each term in the function with respect to x, treating y as a constant. So, we have:
$$f_x = \frac{\partial}{\partial x}(x^{4}) - \frac{\partial}{\partial x}(3 x^{2} y^{3}) + \frac{\partial}{\partial x}(5 y) = 4x^{3} - 6x
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