Let’s solve each exercise step by step.

Exercise 1: Derivatives

Find the derivatives of the following:

(a) $y = \sqrt{1 + \cos x}$

• Use chain rule: $\frac{d}{dx}[\sqrt{u}] = \frac{1}{2\sqrt{u}} \cdot u'$, where $u = 1 + \cos x$.
  $\frac{dy}{dx} = \frac{1}{2\sqrt{1 + \cos x}} \cdot (-\sin x)$ [ \