# 
restart;
f:=t->sqrt(1-t^2);
A:=Int(f(t),t=0..x);
A2:=value(A);
A3:=diff(A2,x);
simplify(A3);
A4:=1/2*1/sqrt(1-x^2)+1/2*sqrt(1-x^2)+1/2*x*1/(2*sqrt(1-x^2))*(-2*x);
simplify(A4);

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