1. (20%) Find $dy/dx$ where

(a) \( \cos (xy) = 1 + \sin y \)
(b) \( y = \int_0^{x^2 -1}(t + 1)^2 e^{t^2 +2t + 1}dt. \)
(c) \( y = \cos^{-1}(2x + 1) \)
(d) \( y = \tanh (1 + e^{2x}) \)