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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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Find the derivative of the given function from first principle \[\] $(x-1)(x-2)$

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Let $f(x) = (x-1)(x-2)$. Accordingly, from the first principle.
$f'(x) = \lim\limits_{h \to 0} \large\frac{f(x+h)-f(x)}{h}$
$ = \lim\limits_{h \to 0} \large\frac{(x+h-1)(x+h-2)-(x-1)(x-2)}{h}$
$ = \lim\limits_{h \to 0} \large\frac{(x^2+hx-2x+hx+h^2-2h-x-h+2)-(x^2-2x-x+2)}{h}$
$ = \lim\limits_{h \to 0} \large\frac{hx+hx+h^2-2h-h}{h}$
$ = \lim\limits_{h \to 0} \large\frac{2hx+h^2-3h}{h}$
$ = \lim\limits_{h \to 0}(2x+h-3)$
$= (2x+0-3)$
$ 2x-3$
answered Apr 7, 2014 by thanvigandhi_1
 

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