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 main purpose of finding the derivative in the context of writing the equation of a line?

Explain the product rule and how it is applied in the given context.

How do you combine like terms after applying the quotient rule?

What is the significance of evaluating F at a specific point when finding the slope?

Describe the process of writing the equation of a line using the slope and a point.