Question

Find the derivative of $f\left(x\right)=x^2-2$ at x = 10

Answer 1

$\text{Let}f\left(x\right)=x^2-2,\text{we have}$

$f^{\prime }\left(x\right)=li{m}_{h\to 0}\frac{f(x+h)-f\left(x\right)}{h}$

$f^{\prime }\left(x\right)=li{m}_{h\to 0}\frac{\left[\right(x+h{)}^2-2]-(x^2-2)}{h}$

$=li{m}_{h\to 0}\frac{x^2+h^2+2xh-2-x^2+2}{h}$

$=li{m}_{h\to 0}\frac{h(h+2x)}{h}=0+2x=2x$

$\text{At}x=10,f^{\prime }10=2\times 10=20$