For some constants a and b, find the derivative of(i) `(x - a) *(x-b)` (ii) `(a x^2+b)^2` (iii) `(x-a)/(x-b)`

Explanation

To find the derivatives of the given functions, we will use the rules of differentiation, including the product rule, chain rule, and quotient rule. Let's solve each part step by step.

### (i) Derivative of \( (x - a)(x - b) \)

Let \( y = (x - a)(x - b) \).

1. **Apply the Product Rule**: The product rule states that if \( y = u \cdot v \), then \( \frac{dy}{dx} = u \frac{dv}{dx} + v \frac{du}{dx} \).
- Here, let \( u = (x - a) \) and \( v = (x - b) \).
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