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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It’s basically saying that you’re differentiating (finding the rate of change) of Y compared to X. For example, if you’re driving a car and you know how far you have traveled over time then you can call distance Y and time X then differentiate Distance over Time to get your speed at any point in time. You can differentiate this again to get your Acceleration. The important part is that this isn’t just your average speed, it’s the formula for calculating your speed at any time over your journey
The Y or X are just the standard names for the variables – you can call them anything you like. In the distance over time example I used, you can call distance D and time T and velocity V then you get V = dD/dT
You could then call acceleration A and get A = dV/dT
The whole idea of calculus is to look at rates of change which is useful for a wide range of applications
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