Why is the derivative of a linear function a constant?

1 Answer
Dec 20, 2015

In order to know, we need to get back to the definition of the derivative.

Explanation:

The derivative of a function #f# at #a# is #lim_(x->a) (f(x) - f(a))/(x-a)# when the limit exists and is finite.

Let's write down that quotient for #f(x) = mx# with #m in RR# without evaluating the limit : #(mx - ma)/(x-a) = m(x-a)/(x-a) = m#. Since #m# is a constant, this will still be true when you will evaluate the limit at #a#.