Use rules in calculus to establish the following rules when
w(t) = u(t) + iv(t)
is a complex-valued function of a real variable t and w'(t) exists:
(a) d/dt w(-t) = - w'(-t) where w'(-t) denotes the derivative of w(t) with respect to t, evaluated at - t;
(b) d/dt [w(t)]2 = 2w(t)w'(t).