Understanding the Constant Rule for Derivatives

This video tutorial explains the constant rule for derivatives, stating that the derivative of a constant is zero. It provides examples with constants like 5, -7, 24, pi, and e, demonstrating that their derivatives are zero. The video also includes a proof using the definition of a derivative to show that the derivative of any constant is zero.

What is the derivative of a constant value?

• The constant itself

• Undefined

• Zero

• One

If y = 5, what is the derivative of y with respect to x?

• 0

• 1

• x

• 5

Which of the following is a constant?

• sin(x)

• pi

• x

• x^2

What is the derivative of f(x) = pi?

• x

• 0

• 1

• pi

Why is the derivative of a constant zero?

• Because constants do not change with respect to x

• Because constants are always positive

• Because constants are always negative

• Because constants are variables

What is the result of differentiating a constant function using the limit definition?

• The limit is zero

• The limit is the constant itself

• The limit is infinite

• The limit is undefined

In the proof using limits, what happens to the expression (f(x + h) - f(x)) as h approaches zero?

• It becomes infinite

• It becomes h

• It becomes zero

• It becomes undefined

What is the derivative of a function f(x) = 8?

• 8

• 1

• 0

• x

Which of the following statements is true about the derivative of a constant?

• It is always equal to the constant

• It is always zero

• It is always one

• It is always undefined

What is the derivative of y = e?

• e

• 1

• 0

• x