Differentiate the following function :
(i) `(x^(2) - 5x + 6)(x-3)` , (ii) `(sqrt(x) + 1/(sqrt(x)))^(2)` , (iii) `(3x^(2) + 2x + 5)/(sqrt(x))`

Explanation

Let's solve each part of the question step by step.

### Part (i): Differentiate \( (x^2 - 5x + 6)(x - 3) \)

1. **Identify the functions**: Let \( u = x^2 - 5x + 6 \) and \( v = x - 3 \).
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 \( u \) and \( v \)**:
- \( \frac{du}{dx} = 2x - 5 \)
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