kill(all)$

load(atrig1)$ load(ntrig)$

van=facebook.com/LearningCalculus$

depends(y,x)$

eqn:'diff(y,x)=cot(x)^2 + tan(y)^2$

result:''(integrate(eqn,x));

f(x,y):=''(rhs(result));

diff(f(x,y),x);

solve(%,diff(y,x));

trigsimp(%);