I have this question and given my answer for second and third derivatives. not sure if its right though
Your image is somewhat squashed up and with no equals. The dy should be ds. This is what I think you meant:
This is correct
This first term is correct but the second bit is not.
But this is not right. The sign is wrong and there shouldn't be a 3 there.
And this has gone completely wrong. You've lost the 3 from the first term and the error above has made the second term wrong too.
I suggest you have a go at d2s/dt^2 again and I'll check again.
d^2s/dt = -3sint - cost
d^3s/dt = -3cost - - sint = -3cost +sint
if this isn't right I don't know what is.