Understanding the Constant Derivative Rule

The video tutorial provides a proof of the constant derivative rule, which states that the derivative of a constant with respect to x is zero. It begins with an introduction to the rule and the limit definition of a derivative. The tutorial then walks through the proof, showing that the function f(x) equals a constant C, leading to the simplification of the limit expression to zero. This demonstrates that the derivative of a constant is indeed zero.

What is the derivative of a constant C with respect to x?

• x

• 0

• 1

• C

Which symbol is used in the limit definition of the derivative in this video?

• Z

• C

• H

• Delta X

In the context of this video, what is the value of f(x) when f(x) is a constant C?

• x

• C

• 0

• H

What happens to the expression C - C in the limit simplification?

• It becomes H

• It becomes 0

• It becomes 1

• It becomes C

What is the result of the limit as H approaches zero for the expression 0/H?

• C

• Infinity

• H

• 0

What does the proof ultimately demonstrate about the derivative of a constant?

• It is equal to zero

• It is equal to the constant itself

• It is undefined

• It is equal to x