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

Explanation

Let's solve the derivatives step by step for each of the given functions.

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

To find the derivative of the product of two functions, we will use the product rule. The product rule states that if you have two functions \( u(x) \) and \( v(x) \), then:

\[
\frac{d}{dx}[u \cdot v] = u \cdot \frac{dv}{dx} + v \cdot \frac{du}{dx}
...