what is the derivative of 1/2 Sec t?

Answer 1

(1/2)sec(t)tan(t)

Answer 2

Let y = (1/2) .sec t = 1 / (2.cos t) = 1 / u
where u = 2 cos t
du / dt = - 2.sin t
dy / du = - 1 / u² = - 1 / (4 cos² t)
dy / dt = 1 / (4 cos² t). 2 sin t
dy / dt = (1/2).tan t.sec t