Calculus I: The Product Rule (Level 1 of 3)

The video tutorial explores the concept of derivatives, focusing on the product rule. It begins by questioning if the derivative of a product is the product of derivatives, which is disproven. The product rule is introduced, stating that the derivative of a product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first. Examples are provided, including products of more than two functions, and the application of the product rule to quotients. The tutorial concludes with complex examples, emphasizing the importance of consistency in function assignment.

Explain why the derivative of a product is not simply the product of the derivatives.

What is the derivative of a product of two functions according to the product rule?

What are the key components of the product rule as stated in the text?

How can the product rule be extended to cover products involving more than two functions?

What is the significance of the order of functions when applying the product rule?

Describe the process of finding the derivative of the function RV X = X^3 * E^X using the product rule.

What is the first step in applying the product rule to find the derivative of two functions?

How do you rewrite a quotient of two functions to apply the product rule?

In the example of finding the derivative of P of X = (X + 3)(X^2 - 5X + 2), what steps are taken to apply the product rule?

What is the final expression for the derivative of the function involving three functions multiplied together?