Understanding the Product Rule

The video tutorial introduces the product rule, a fundamental method for evaluating derivatives. It explains that if a function is expressed as a product of two functions, its derivative can be found using the product rule. The rule involves taking the derivative of one function while keeping the other unchanged, and then adding the product of the first function and the derivative of the second. The tutorial provides an example using the functions x squared and sine of x, demonstrating how to apply the product rule to find the derivative.

What is the main topic discussed in the video?

• Integration by parts

• Chain rule

• Product rule

• Quotient rule

Which of the following is a fundamental way of evaluating derivatives?

• Difference rule

• Constant rule

• Product rule

• Sum rule

In the product rule, if you have a function expressed as f(x) * g(x), what do you need to find?

• The product of f(x) and g(x)

• The integral of f(x) * g(x)

• The sum of f(x) and g(x)

• The derivative of f(x) * g(x)

What is the derivative of f(x) in the product rule formula?

• f'(x) * g'(x)

• f(x) * g(x)

• f'(x) * g(x)

• f(x) * g'(x)

In the example given, what is f(x) set to?

• x^3

• sin(x)

• x^2

• cos(x)

What is g(x) set to in the example?

• tan(x)

• sin(x)

• cos(x)

• x^2

What is the derivative of x^2 using the power rule?

• x

• 2x

• 2x^2

• x^2

What is the derivative of sin(x)?

• cos(x)

• -cos(x)

• -sin(x)

• tan(x)

What is the final expression for the derivative of x^2 * sin(x) using the product rule?

• x^2 * sin(x) + 2x * cos(x)

• x^2 * cos(x) + 2x * sin(x)

• 2x * sin(x) + x^2 * cos(x)

• 2x * cos(x) + x^2 * sin(x)

What is the purpose of applying the product rule in the example?

• To evaluate the function at a point

• To find the integral of the function

• To find the derivative of the function

• To simplify the function