vector r(t) = sin(t)i + 1/2cos(2t)j + 1/2 t^2k.

Find:

a.(derivative). r'(t)

b.(second derivative). r"(t)

c. (Dot product) r'(t) r"(t)

d. d/dt [r(w(t))] and w(t) = 2t

e. (Cross product) r'(t) x r"(t)