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

1 Answer
Nov 11, 2017

Answer:

#"see explanation"#

Explanation:

#"differentiating from "color(blue)"first principles"#

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

#"the aim is to eliminate h from the denominator"#

#f'(x)=lim_(hto0)(2(x+h)+6-(2x+6))/h#

#color(white)(f'(x))=lim_(hto0)(cancel(2x)+2hcancel(+6)cancel(-2x)cancel(-6))/h#

#color(white)(f'(x))=lim_(hto0)(2cancel(h))/cancel(h)=2#