$$y^2=2px$$ $$ \Rightarrow 2ydy=2pdx $$
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?

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?

anonymous · Answer

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

anonymous · Answer

here is a link this is called differentials chew on it

anonymous · Answer

Oh differentials- I wasn't thinking!