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Basically, derivatives can be written as (dy/dx) in Leibniz's notation, but I remember my teacher saying that it's just a symbol and shouldn't be used like two variables (dy and dx)...

However, when there's some integral and inside it, there's a (dy/dx) * (dx), the teacher says we can cancel the two dx, which contradicts what he said earlier.

Also, when we wish to find the integral of (dy/dx) = x, he said we can multiply by dx on both sides, which of course is also confusing me...

So can you guys help me out, and explain these things to me?

Thanks very much :D