Why is the derivative of a linear function a constant?

1 Answer
Topscooter
Dec 20, 2015

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

Explanation:

The derivative of a function ff at aa 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.

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