Use

f$($x$)=$ x$2-3$x

to find the derivative using the definition.

$-$a$$b$$c$$dEvaluate

f$($x $+$ h$)$

a$.$

$2$x $-3$

$-$a$$b$$c$$dExpand

f$($x $+$ h$)-$ f$($x$)$h

$$

b$.$

x$2+2$xh $+$ h$2-3$x $-3$h

$-$a$$b$$c$$dSimplify

$$

f$($x $+$ h$)-$ f$($x$)$h

$$

c$.$

$$

x$2+2$xh $+$ h$2-3$x $-3$h $-$ x$2+3$xh

$$

$-$a$$b$$c$$dTake the limit

$$lim$$h $0$

f$($x $+$ h$)$ f$($x$)$h

$$

d$.$

$2$x $+$ h $-3$