Question

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

Answer 1

`"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`