Understanding the Constant Multiple Derivative Rule

This video tutorial provides a proof of the constant multiple derivative rule, which states that the derivative of a constant times a function is the constant times the derivative of the function. The proof uses the limit definition of the derivative, demonstrating how to apply it to a function multiplied by a constant. The process involves factoring out the constant from the expression and simplifying it to reach the final result. The tutorial concludes by confirming the rule through this methodical approach.

What is the constant multiple derivative rule?

• The derivative of a sum of functions

• The derivative of a product of two functions

• The derivative of a constant times a function

• The derivative of a quotient of two functions

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

• Epsilon

• Delta X

• H

• Theta

What is the first step in applying the limit definition to C * f(x)?

• Multiplying the function by a variable

• Factoring out the constant C

• Subtracting a constant from the function

• Adding a constant to the function

Why can the constant C be factored out of the limit?

• Because C is a derivative

• Because C is a variable

• Because C is a constant

• Because C is a function

What does the limit of the difference quotient equal in the proof?

• f(x)

• C * f'(x)

• C * f(x)

• f'(x)

What is the final result of the proof for the derivative of C * f(x)?

• f(x)

• C * f'(x)

• f'(x)

• C * f(x)