help with this calc question?

Question

r(t)=(4 COS t, (sqrt 2)*Sin t)
is the position vector of a particle moving in the plane at time t. Find:

a. the velocity and acceleration vectors
b. the speed of the particle at t=pi/4

Answer 1

v(t)=<-4sin t, (sqrt2)*cost>
a(t)=<-4cos t, (sqrt2)*-cos t>
B) <-2 (sqrt 2), 1>

Answer 2

Question a)
r = 4.cos t + i √2 sin t
dr / dt = - 4.sin t + √2 i cos t (velocity vector)
d²r / dt² = - 4 cost - √2 i sin t (accn. vector)
Question b)
At t = π / 4:-
dr / dt = - 4.(1/√2) + √2 i .(1 / √2)
dr / dt = - 4.(1/√2) + i
dr / dt = - 2.√2 + i = speed at t = π / 4