# Find the derivative of $x^2-2$ at $x = 10$

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