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The deriviative of f(x) = x is 1 because the slope of the function f(x) = x is 1.
Recall the slope-intercept form of a line. The equation f(x) = x can also be stated as y = mx+b, where m is 1 and b is 0. The slope is m, or 1, and the deriviative of f(x) is the slope of f(x), which is m or 1, in this case.
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