Question

Why is the derivative of a linear function a constant?

Answer 1

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`.