What is a Derivative? Deriving the Power Rule

The video tutorial introduces the concept of differentiation, explaining it as the process of finding the slope of a tangent line to a curve at a given point. It covers the basic understanding of derivatives, illustrating how they represent the rate of change of a function. The tutorial provides examples of calculating derivatives for constant, linear, and quadratic functions, and introduces the power rule, a simplified method for finding derivatives of functions with positive integer exponents.

What does the derivative of a function at a particular point tell us?

• The maximum value of the function

• The average value of the function

• The rate of change of the function at that point

• The value of the function at that point

How is the slope of a tangent line related to the derivative of a function?

• It is unrelated to the derivative

• It is the reciprocal of the derivative

• It is the same as the function's value

• It is equal to the derivative at that point

What happens to the slope of the secant line as the second point approaches the first point?

• It remains constant

• It becomes infinite

• It becomes the slope of the tangent line

• It becomes zero

What is the derivative of a constant function?

• One

• Zero

• The constant itself

• Undefined

When finding the derivative of x squared, what is the resulting expression?

• 2x

• 3x squared

• x

• x squared

What is the power rule used for in differentiation?

• Finding the integral of a function

• Calculating the average rate of change

• Simplifying the process of finding derivatives of polynomial functions

• Determining the maximum value of a function

According to the power rule, what is the derivative of x cubed?

• 3x squared

• 3x

• x squared

• x cubed