[g(x)/f(x)]'={g(x)*[1/f(x)]'=
=g'(x)*[1/f(x)]+g(x)*[1/f(x)]'=
=g'(x)*[1/f(x)]+g(x)*{[f(x)]^(-1)}'=
=g'(x)*[1/f(x)]+g(x)*{(-1)[f(x)]^(-1-1)}*f'(x)}=
=g'(x)f(x)/[f(x)]^2-g(x)f'(x)/[f(x)]^2=
=[g'(x)f(x)-g(x)f'(x)]/[f(x)]^2
[g(x)/f(x)]'={g(x)*[1/f(x)]'=
=g'(x)*[1/f(x)]+g(x)*[1/f(x)]'=
=g'(x)*[1/f(x)]+g(x)*{[f(x)]^(-1)}'=
=g'(x)*[1/f(x)]+g(x)*{(-1)[f(x)]^(-1-1)}*f'(x)}=
=g'(x)f(x)/[f(x)]^2-g(x)f'(x)/[f(x)]^2=
=[g'(x)f(x)-g(x)f'(x)]/[f(x)]^2