What is the dot in "$1.2.4$"?

It is a quite common notation, if used, for multiplication, i.e.

$$5.3=5\cdot3=5\times3=15$$

In your case

$$dy/dx.dx/dt=\frac{dy}{dx}\times\frac{dx}{dt}$$ and $$e^x=1+x+\frac{x^2}{1.2}+\frac{x^3}{1.2.3}+\cdots=1+x+\frac{x^2}{1\times2}+\frac{x^3}{1\times2\times3}+\cdots$$

Sometimes a dot is used for multiplication. Cf. this Wikipedia article.