Limit Definition of Derivative

Sample question from math.net.



1. The derivative of x^2 is a term, it is 2x. Can the derivative be a constant?

2. If I wanted to find the derivative at the point
(2, 4), I simply let x = 2 for 2x to get 4. Yes? How about for the point (a, b)? I simply let x = a for 2x to get 2a. Yes?

 

The derivative of x^2 is 2x:


so rule is:


if y=3x, derivative is

 

So, the derivative can be a term or a constant.