kill(all)$

van=facebook.com/LearningCalculus$

f(x):=(%e^x-cos(x));

g(x):=log(x)^x-cos(x);

h(x):=f(x)/g(x)$ h(x);

limit(h(x),x,0);

diff(h(x),x);

limit(diff(f(x),x,1)/diff(g(x),x,1),x,0);