I'm a uni student trying to derive the acceleration vector given the position vector on an online service my uni uses.
I'm 90% sure my answer is correct, so I think the website may have incorrectly marked me.
The position vector is $\mathbf{s}(t) = \langle 5t, e^{-t} + 4\sin(t), e^{-t} + 4\cos(t) \rangle$. I got the velocity vector as $\mathbf{v}(t) = \langle 5, -e^{-t} + 4\cos(t), -e^{-t} - 4\sin(t) \rangle$ and the acceleration vector as $\mathbf{a}(t) = \langle 0, e^{-t} - 4\sin(t), e^{-t} - 4\cos(t) \rangle$. The website marked me as correct for the velocity vector and correct for the i component for the acceleration vector, but incorrect for the $\mathbf{j}$ and k components of the acceleration vector.
Am I crazy or did the website mark me incorrectly?
Your answer is correct, the website is wrong.