>>529
g'(t) = x'f_x + y'f_y = 3t^2f_x + 4t^3f_y

g''(t) = x''f_x + y''f_y + x'(f_x)' + y'(f_y)'
= x''f_x + y''f_y + x'(x'f_xx + y'f_xy) + y'(x'f_yx + y'f_yy)
= 6tf_x + 12t^2f_y + 9t^4f_xx + 24t^5f_xy + 16t^6f_yy