Find the derivative of x2– 2 at x = 10

Let f(x) = x²-2 Accordingly,

\( f'(10)=\lim\limits_{h \to 0}\dfrac{f(10+h)-f(10)}{h}\)

\(\lim\limits_{h \to 0}\dfrac{[(10+h)^2]-(10^2-2)}{h}\)

\( \lim\limits_{h \to 0}\dfrac{10^2+2.10h+h^2-2-10^2+2}{h}\)

\( \lim\limits_{h \to 0}\dfrac{20h+h^2}{h}\)

\( \lim\limits_{h \to 0}(20+h)=20+0=10\)