6. (20 points) Sections 3.1-3.5, 3.7 Differentiate the following functions, state the regions where the functions are analytic. a. cos(e*) b. 1 ez +1 c. Log (z+1) (Hint: To find where it is analytic, you may let z = x + iy.) d. tanh (z), use z = 0 and the negative real axis as branch cut for the logarithmic function involved. For calculating the derivative, you need to show intermediate steps, since the answer is already given in the textbook.