How to write the equation of a tangent line by taking the derivative using product

The video tutorial explains how to find the derivative of a function to determine the slope at a given point. It covers the application of the product rule and the process of combining like terms to simplify expressions. The tutorial also demonstrates how to calculate the slope at a specific point and use it to write the equation of a line in slope-intercept form.

What is the primary goal when writing the equation of a line in this context?

• To calculate the area under the curve

• To determine the slope at a given point

• To find the y-intercept

• To identify the x-intercept

Which rule is applied to find the derivative of the product of two functions in this section?

• Quotient Rule

• Product Rule

• Chain Rule

• Power Rule

What is the result of combining like terms after applying the quotient rule?

• X^3 - 3X + 1

• X^3 + 3X^2 - 3X + 1

• 4X^3 + 6X^2 - 6X - 5

• 3X^2 - 3

How is the slope at a specific point determined in this section?

• By calculating the area under the curve

• By evaluating the derivative at that point

• By using the midpoint formula

• By finding the y-intercept

What is the final form of the equation of the line derived in this section?

• Y = -X - 1

• Y = -X + 3

• Y = X + 3

• Y = X - 1