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. Product Rule: w'(t) = u'(t)v(t) + u(t)v'(t)
b. Quotient Rule: w'(t) = (u'(t)v(t) - u(t)v'(t)) (v(t))²
c. Chain Rule: w'(t) = u'(t)v(t) + u(t)v'(t) + iv'(t)
d. Power Rule: w'(t) = iu(t)v(t)