syms t;

f(t) = (6*(1+2*t^2 )*(t^3 - t)^2) / (sqrt(t+5*t^2)*(4*t)) + (sqrt(1+2*t)) / (t + sqrt(1+t^2));

f_t = diff(f,t);

%simplify(f_t,Steps=100);

disp(f_t);