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The notation $df/dx$ motivates thinking of tiny vertical changes paired with tiny horizontal changes, and informally canceling $dx$ helps intuition. However, it is misleading because the derivative is defined by a limit, not by dividing two ordinary numbers.

Conditions: Interpreting the differential notation in the context of the theorem.; Understanding the formal definition of the derivative.

The notation $df/dx$ motivates thinking of tiny vertical changes paired with tiny horizontal changes, and informally canceling $dx$ helps intuition. However, it is misleading because the derivative is defined by a limit, not by dividing two ordinary numbers.

Conditions: Interpreting the differential notation in the context of the theorem.; Understanding the formal definition of the derivative.