Limit Definition of Derivative

[nycmathguy]

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?

 

[MathLover1]

The derivative of x^2 is 2x:

so rule is:

if y=3x, derivative is

 

[nycmathguy]

The derivative of x^2 is 2x:
View attachment 3365

so rule is:
View attachment 3364

if y=3x, derivative is

View attachment 3366

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