Calculus I: The Product Rule (Level 2 of 3)

This video tutorial covers advanced examples of using the product rule in calculus. It begins with a basic introduction to the product rule, followed by examples involving differentiable functions, power functions, rational functions, and exponential functions. The video also demonstrates how to evaluate derivatives at specific points using given function values. The tutorial concludes with a summary and a preview of the next topic, which involves using graphs to find derivatives.

What is the product rule in calculus?

How do you find the derivative of a function defined as the product of two differentiable functions?

Explain the process of applying the product rule to the function R(x) = p(x) * q(x).

What is the final expression for the derivative of R(x) = x^2 * q(x) + p(x)?

How do you differentiate the term q(x) / x using the product rule?

What steps are involved in finding the derivative of f(x) = g(x) * h(x) given specific values?

What is the significance of knowing the values of functions and their derivatives at a specific point?

Describe how to evaluate the derivative of a function at a specific point using given values.

How does the product rule apply to the function f(x) = e^x * h(x)?

What is the final answer when evaluating the derivative of f at x = 0 for f(x) = e^x * h(x)?