EXAMPLE $4$ Find the derivative of the function

f$($x$)=$ x$26$x $+2$

at the number a$.$

SOLUTION From the definition we have

f$\text{'}($a$)=$lim$$h $0$

f$($a $+$ h$)$ f$($a$)$h

$=$lim$$h $0$

$6($a $+$ h$)+2$

$[$a$26$a $+2]$h

$=$lim$$h $0$

a$2+$

$6$a $6$h $+2$ a$2+6$a $2$h

$=$lim$$h $0$

h

$=$lim$$h $0$

$=$

$.$