D^{(n+1)}( f_{n+1}) = D\left( xD^{(n)}(f_n) + nD^{(n-1)}(f_n)\right)

it reminds me the pattern of a derivative of a complex function:

f(x)=sin(x^2)

f'(x)=cos(x^2)*2x

is it like that

can you explain me the equation
in this terms
i cant see in it
what the derivative of the function
and whats the derivative of the inner function
??