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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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For some constants $a$ and $b$, find the derivative of \[\] $ \large\frac{(x-a)}{(x-b)}$

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Let $f(x) = \large\frac{(x-a)}{(x-b)}$
$ f'(x) = \large\frac{d}{dx}$$ \bigg( \large\frac{x-a}{x-b} \bigg)$
By quotient rule,
$ f'(x) = \large\frac{(x-b)\large\frac{d}{dx}(x-a)-(x-a)\large\frac{d}{dx}(x-b)}{(x-b)^2}$
$ = \large\frac{(x-b)(1)-(x-a)(1)}{(x-b)^2}$
$ = \large\frac{x-b-x+a}{(x-b)^2}$
$ = \large\frac{a-b}{(x-b)^2}$
answered Apr 9, 2014 by thanvigandhi_1

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