kill(all)$

van=facebook.com/LearningCalculus$

Q(x,y):= y = x/(a+x/(b+y));

depends(y,x)$

f(x):=''(solve(Q(x,y),y));

fp(x):=''(diff(f(x),x));

van=facebook.com/LearningCalculus$

eqn2: y = x/(a+x/(b+x/(a+x/(b+y))));

depends(y,x)$

h(x):=''(solve(eqn2,y));

hp(x):=''(diff(h(x),x));

diff(eqn2,x);

g(x,theta):=substitute(sin(theta),b,substitute(cos(theta),a,f(x)))$

gp(x,theta):=substitute(sin(theta),b,substitute(cos(theta),a,fp(x)))$ gp(x,t)$

first(gp(x,theta)); second(gp(x,theta));