kill(all);

area:abs(((((sin((π*5/24))*((cos((π*5/24))*x)+(cos((π*29/24))*x*2))*(-1))+(sin((π*17/24))*(((x)^(2)+((((cos((π*5/24))*x)+(cos((π*29/24))*x*2)))^(2)*(-1))))^(1/2)))*x*1/2)+(((sin((π*5/24))*((cos((π*5/24))*x)+(cos((π*29/24))*x*2))*(-1))+(sin((π*17/24))*(((x)^(2)+((((cos((π*5/24))*x)+(cos((π*29/24))*x*2)))^(2)*(-1))))^(1/2)))*(x+((cos((π*19/24)))^(2)*x*(-1))+(abs(sin((π*19/24)))*cos((π*31/24))*x*(-1)))*(-1/2))+(((cos((π*19/24))*sin((π*19/24))*x*(-1))+(abs(sin((π*19/24)))*sin((π*31/24))*x*(-1)))*x*(-1/2))+(((cos((π*19/24))*sin((π*19/24))*x*(-1))+(abs(sin((π*19/24)))*sin((π*31/24))*x*(-1)))*(x+(cos((π*5/24))*((cos((π*5/24))*x)+(cos((π*29/24))*x*2))*(-1))+(cos((π*17/24))*(((x)^(2)+((((cos((π*5/24))*x)+(cos((π*29/24))*x*2)))^(2)*(-1))))^(1/2)))*1/2)));

solve(area,x);

diff(%,t);

radcan(area);

depends(x,t);

dAdt:diff(area,t)=1;

fullratsimp(solve(dAdt,diff(x,t)));