For some constant $a$ and $b$ , find the derivative of the following functions:
$\frac{x - a}{x - b}$ .

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Solution

Let $f (x) = \frac{(x - a)}{(x - b)}$
Thus by quotient rule,
$f^{^{'}} (x) = \frac{(x - b) \frac{d}{d x} (x - a) - (x - a) \frac{d}{d x} (x - b)}{{(x - b)}^{2}}$
$= \frac{(x - b) (1) - (x - a) (1)}{{(x - b)}^{2}}$
$= \frac{x - b - x + a}{{(x - b)}^{2}} = \frac{a - b}{{(x - b)}^{2}}$

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