We know that

$\dfrac d {dx} y = \dfrac {dy}{dx}=\dfrac {\dfrac {dy}{dt}}{\dfrac {dx}{dt}}$

so it stands to reason that

$\dfrac d {dx} \dfrac {dy}{dx} = \dfrac {\dfrac d {dt} \dfrac {dy}{dx}}{\dfrac {dx}{dt}}=$

$-\dfrac {\sin(2t+1)+2\cos(t)}{(2t+1)^3}$