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
In differential equations you can do this, during separation of variables which usually precedes an integration iirc:
(dy/dx) = x^2 /y^2
y^2 (dy) = x^2 (dx)
Then you can integrate to find y in terms of x
The reason people say it’s not a fraction is because when you get into higher order derivatives, they don’t behave the same way as a simple fraction would. So basically it’s not *always* a fraction, and if you don’t 100% know what you’re doing it’s best to treat it as if it’s not a fraction
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