Differential of the second order of function `y=f(x)` is differential of first differential of the function: `d^2y=d(dy)`.
Differential of the third order of function `y=f(x)` is differential of second differential of the function: `d^3y=d(d^2y)`.
In general, differential of n-th order of function `y=f(x)` is differential of its `(n-1)-th` differential: `d^ny=d(d^(n-1)y)`.
When we calculate differentials it is important to remember that `dx` is arbitrary and independent from `x` number. So, when we differentiate with respect to `x` we treat `dx` as constant.
In general `color(blue)(d^(n)y=y^((n))dx^n)`.
From this we have that `y^((n))=(d^n y)/(dx^n)`.
From now we can treat this symbol as ratio.