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if i said differentiate y=2x does that mean take the derivative? or what exactly?

Mathematics
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yes
well what is it then when you get dy by it self? and have something like dy = 2dx
separation of variables. take the integral of each.

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Other answers:

something like the differential?
the derivative of a straight line is simply the slope
Differentiate \[y=2x\]\[\frac{ dy }{ dx }=2\]\[dy=2dx\]that looks familiar Integrate:\[\int\limits dy=\int\limits 2 \space dx\]\[y=2x+C\]
\[\int\limits dy = \int\limits 2xdx \]
so differentiate just means put the dy by it self?
<.< using words that are so similar is not a good idea
you are basically taking the antiderivative, which in essence is differentiating.

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