How to take the derivative using the product rule with sine

The video tutorial explains the process of finding derivatives, focusing on the constant rule and product rule. It begins with an introduction to derivatives, followed by a detailed explanation of the product rule. The instructor sets up the derivative calculation and then performs and simplifies the calculations, ensuring students understand each step.

What is the main focus of the first section of the video?

• Solving complex equations

• Explaining the constant rule and separation by subtraction

• Graphing functions

• Understanding the product rule

When do you need to apply the product rule in derivatives?

• When multiplying two functions

• When terms are separated by addition

• When using the constant rule

• When dealing with a single variable

Which rule is used to find the derivative of 2X times cosine of X?

• Chain rule

• Quotient rule

• Product rule

• Constant rule

What is the derivative of 2X according to the video?

• 2

• X

• 0

• 2X

What happens to the expression after applying the product rule and simplifying?

• It becomes a constant

• It simplifies

• It becomes more complex

• It remains unchanged