Use the product rule to take the derivative of an exponential equation

The video tutorial explains the product rule in calculus, demonstrating how to take the derivative of a product of functions. It covers the steps involved, including taking derivatives of individual functions and simplifying the resulting expression by factoring. The tutorial also highlights the importance of recognizing factoring opportunities, especially in multiple-choice scenarios.

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

• Take the derivative of the second function.

• Add the two functions together.

• Multiply the two functions together.

• Take the derivative of the first function.

When simplifying expressions, what is a common term that can be factored out in this context?

• X squared

• E to the X

• The derivative of the second function

• The sum of the functions

What is left after factoring out E to the X in the given expression?

• E to the X

• X + 2

• 2 + X

• X squared

Why is it important to look for factoring opportunities in multiple-choice problems?

• To avoid using the product rule

• To simplify the problem and find the correct answer more easily

• To make the problem more complex

• To increase the number of steps in the solution

In non-multiple choice problems, why might factoring still be useful?

• It allows skipping steps in the solution.

• It helps in checking the correctness of the solution.

• It makes the problem more challenging.

• It is not useful in non-multiple choice problems.