It’s pretty common to hear that dy/dx isn’t a fraction, but if that’s the case then why do we treat as such in a differential equation or an integral? For example, if dy/dx = f(x), then how can we just write it as dy= f(x)dx as though it’s a fraction?
In: Mathematics
They kind-of are, but notation makes things confusing. dy and dx are not really values, but operations. The d in dy and dx is suppose to be a lowercase greek letter delta. Delta is a commonly used shorthand in math and physics for the amount of change in something. This means that dy/dx is the ratio of the amount of change in y to the amount of change in x, which is the derivative. But because they are operations on variables instead of actual variables themselves, there are slightly different rules for when they can be introduced and manipulated.
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