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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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Find the derivative of $x^2-2$ at $ x = 10$

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Let $ f(x) = x^2-2$. Accordingly,
$ f'(10) = \lim\limits_{ h \to 0} \large\frac{f(10+h)-f(10)}{h}$
$ \lim\limits_{h \to 0} \large\frac{[ (10+h)^2-2]-(10^2-2)}{h}$
$ \lim\limits_{h \to 0} \large\frac{10^2+2.10.h+h^2-2-10^2+2}{h}$
$ \lim\limits_{h \to 0} \large\frac{20h+h^2}{h}$
$ \lim\limits_{h \to 0} (20+h)=(20+0)=20$
Thus, the derivative of $ x^2-2$ at $ x = 10\: is \: 20$
answered Apr 7, 2014 by thanvigandhi_1
 
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