Question

\[y^2=2px\] \[ \Rightarrow 2ydy=2pdx \]
How is this achieved at? I've always gone with calculating
\[ 2y\frac{dy}{dx}=2p \] and multiplying both sides by dx. But I know that's heresy.

What's the official story as to how it's arrived at?

Answer 1

I've always found it odd how it seems plucked out of thin air

Answer 2

here is a link this is called differentials chew on it

Answer 3

Oh differentials- I wasn't thinking!