Jakob Bernoulli’s solution I'm reading this.
It says,
from $ds^2 = dx^2 + dy^2$, we can get
$2dsd^2s =2dxd^2x $
I cannot understand this process. 
Please give me some references.(simpler is better)

It is just the chain rule with fixed $dy$, i.e $d (ds^2) = 2 ds \times d(ds) = 2 \hspace{2pt} ds \hspace{2pt} d^2 s$.
Similar for $dx$, and $d(dy) = 0$ as $dy$ is fixed.
