Find d2y/dx2, as a function of t, for the given the parametric equations: x=4−3cos(t), y=9+cos3(t)

Answer 1

dy/dx = (dy/dt)/(dx/dt) = - 3sin3t/3sint = - sin3t/sint

d²y/dx² = d/dx(dy/dx) = d/dt(-sin3t/sint)/(dx/dt) = - d/dt(sin3t/sint)/(3sint) = -[(3cos3tsint - costsin3t)/sin²t]/(3sint) = (costsin3t - 3cos3tsint)/(3sin³t)

Answer 2