My textbook says it’s not a fraction but defined in terms of the limit of a fraction, what does this actually mean? I’m generally having trouble understanding the notation, particularly in the context of implicit differentiation.
Thanks.
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Imagine you are driving on a high way. Let’s say y is the location of your car and x is the time that you have been driving. You can brake, make turns, or change lines. All these are changes made in your location y as a function of the time x. A fraction of y over x would be your speed. dy/dx doesn’t only describe your speed. It breaks your journey into an infinite amount of time points, and describes how exactly your car would go from point A to point B at any single point of time.
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