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`

Explanation

Let's find the derivatives of the given functions step by step.

### (i) Derivative of `sin x cos x`

1. **Identify the functions**: Let \( u = \sin x \) and \( v = \cos x \).
2. **Apply the product rule**: The product rule states that if \( y = uv \), then \( \frac{dy}{dx} = u \frac{dv}{dx} + v \frac{du}{dx} \).
3. **Differentiate**:
- \( \frac{du}{dx} = \cos x \)
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