# How do you find the derivative of the function f(x)=x^2-3x using f(x+h)-f(x)/h?

Apr 20, 2015

Know that:

$f ' \left(x\right) = {\lim}_{h \rightarrow 0} \frac{f \left(x + h\right) - f \left(x\right)}{h}$

$= {\lim}_{h \rightarrow 0} \frac{{\left(x + h\right)}^{2} - 3 \left(x + h\right) - \left({x}^{2} - 3 x\right)}{h}$

$= {\lim}_{h \rightarrow 0} \frac{{x}^{2} + 2 x h + {h}^{2} - 3 x - 3 h - {x}^{2} + 3 x}{h}$

$= {\lim}_{h \rightarrow 0} \frac{{h}^{2} + 2 x h - 3 h}{h}$

$= {\lim}_{h \rightarrow 0} \frac{h \left(h + 2 x - 3\right)}{h}$

$= {\lim}_{h \rightarrow 0} h + 2 x - 3$

$= 2 x - 3$