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**dx**** **in the denominator of this "fraction" specifically tells you "with respect to x". It becomes more important if you're doing functions of multiple variables. If you have a function f(x, y, z), then f ' (x, y, z) doesn't tell you which derivative to do (wrt x, y or z). However, if you say d/dx[ f(x, y, z)], then you know specifically to do the derivative with respect to x, considering y and z as constants.

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