# How do you use the definition of a derivative to find the derivative of f(x)=2x+6?

Nov 11, 2017

$\text{see explanation}$

#### Explanation:

$\text{differentiating from "color(blue)"first principles}$

•color(white)(x)f'(x)=lim_(hto0)(f(x+h)-f(x))/h

$\text{the aim is to eliminate h from the denominator}$

$f ' \left(x\right) = {\lim}_{h \to 0} \frac{2 \left(x + h\right) + 6 - \left(2 x + 6\right)}{h}$

$\textcolor{w h i t e}{f ' \left(x\right)} = {\lim}_{h \to 0} \frac{\cancel{2 x} + 2 h \cancel{+ 6} \cancel{- 2 x} \cancel{- 6}}{h}$

$\textcolor{w h i t e}{f ' \left(x\right)} = {\lim}_{h \to 0} \frac{2 \cancel{h}}{\cancel{h}} = 2$