Question

How do you find the derivative of the function `f(x)=mx+b`?

Answer 1

using the definition of differentiation we have `f'(x)=m`

Explanation:

The definition of the derivative is:

`f'(x)=Lim_(hrarr0)(f(x+h)-f(x))/h`

`f'(x)=Lim_(hrarr0)(m(x+h)+b-(mx+b))/h`

`f'(x)==Lim_(hrarr0)(mx+mh+b-mx-b)/h`

`f'(x)==Lim_(hrarr0)(cancel(mx)+mh+cancel(b)-cancel(mx)-cancel(b))/h`

`f'(x)==Lim_(hrarr0)(mcancel(h))/cancel(h)`

`f'(x)==Lim_(hrarr0)(m)`

`:.f'(x)=m`