kill(all)$

load(ntrig)$ load(atrig1)$

van=facebook.com/LearningCalculus$

f(x):=sqrt((x^2-1)/(x^2+1));

[a,f(a)];

[b,f(b)];

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

fp(a);

fp(b);

g(a,b):=(π+(atan((((((1+(a)^(2)))^(3/2)*(((-1)+(a)^(2)))^(1/2)*b)+(((1+(b)^(2)))^(3/2)*(((-1)+(b)^(2)))^(1/2)*a*(-1)))*(((b*a*4)+(((1+(b)^(2)))^(3/2)*((1+(a)^(2)))^(3/2)*(((-1)+(b)^(2)))^(1/2)*(((-1)+(a)^(2)))^(1/2))))^((-1))*2))*(-1)));

G(a,b):= ''(trigsimp(g(a,b))) - %pi/2;

d(a,b):= (((((a*(-1))+b))^(2)+(((((1+(a)^(2)))^((-1/2))*(((-1)+(a)^(2)))^(1/2)*(-1))+(((1+(b)^(2)))^((-1/2))*(((-1)+(b)^(2)))^(1/2))))^(2)))^(1/2);

D(a,b):=radcan(d(a,b));

G(x,y);

D(x,y);