Find the derivative of the following functions:
(i) `sin x cos x`
(ii) `sec x`
(iii) `5 sec x + 4 cos x`
(iv) `cos e c x`
(v) `3 cot x + 5 cos e c x`
(vi) `5 sin x -6 cos x + 7`

Explanation

To find the derivatives of the given functions, we will apply the rules of differentiation, including the product rule, quotient rule, and basic derivatives of trigonometric functions. Let's go through each function step by step.

### (i) Find the derivative of \( f(x) = \sin x \cos x \)

Using the product rule, which states that if \( f(x) = u(x)v(x) \), then \( f'(x) = u'v + uv' \):

1. Let \( u = \sin x \) and \( v = \cos x \).
2. Find \( u' = \cos x \) and \( v' = -\sin x \).
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