Say y=f(x). To my understanding, the meaning of the derivative dydx=f′(x) in English would be something like "the change in y with respect to the change in x at a given point is f′(x)."
After a symbolic manipulation of the derivative where we "multiply" both sides by dx, we get the differential dy=f′(x)dx. My question is, what does the differential actually mean (verbally), and how is it different from the derivative?
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