f(x):=x^4;

g(x):=sin(x)^2-x^2;

u(x):=diff(f(x),x,1)/diff(g(x),x,1)$ u(x);

v(x):=diff(f(x),x,2)/diff(g(x),x,2)$ v(x);

w(x):=diff(f(x),x,3)/diff(g(x),x,3)$ w(x);

y(x):=diff(f(x),x,4)/diff(g(x),x,4)$ y(x);

limit(y(x),x,0);