Compute derivative of (i) `f (x) = sin 2x` (ii) `g(x) = cot x`

Explanation

To compute the derivatives of the given functions, we will use the rules of differentiation, specifically the chain rule and the quotient rule.

### Part (i): Compute the derivative of \( f(x) = \sin(2x) \)

1. **Identify the function and the rule to use**: The function is \( f(x) = \sin(2x) \). We will use the chain rule for differentiation.

2. **Differentiate the outer function**: The derivative of \( \sin(u) \) with respect to \( u \) is \( \cos(u) \). Here, \( u = 2x \).

...