Answer
$f'(x)=m$
Work Step by Step
$f(x)=mx+b$
Derivative of a function using the definition: $f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}$
To find $f(x+h)$, wherever you find $x$ in the function, substitute $x+h$
$f(x+h)=m(x+h)+b=mx+mh+b$
Let's plug in the components of the formula:
$f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}=\lim\limits_{h \to 0}\dfrac{mx+mh+b-mx-b}{h}=\lim\limits_{h \to 0}\dfrac{mh}{h}=\lim\limits_{h \to 0}\ m=m$
$f'(x)=m$
