Worked example: Product rule with table | Derivative rules | AP Calculus AB | Khan Academy

TL;DR

This video explains how to evaluate the derivative of the product of two functions and demonstrates the process using specific function values.

Transcript

• [Voiceover] The following tables lists the values of functions f and h, and of their derivatives, f prime and h prime for x is equal to three. So all this is telling us, with x is equal to three, the value of the function is six, f of three is six, you could view it that way. h of three is zero, f prime of three is six, and h prime of three is fo... Read More

Key Insights

• 🎮 The video demonstrates how to apply the product rule to find the derivative of the product of two functions.
• ❓ Evaluating the derivative involves substituting specific function values into the derivative formula.
• 📏 The product rule is a useful tool in calculus for finding the derivative of a product of functions.
• ❓ The derivative of a product of functions can be evaluated at a specific value using the given function values.

Questions & Answers

Q: What is the purpose of the video?

The video explains how to evaluate the derivative of the product of two functions at a specific value using the product rule in calculus.

Q: How is the product rule applied in finding the derivative of the product of functions?

The product rule states that to find the derivative of the product of two functions, you multiply the derivative of the first function by the second function and add it to the product of the first function and the derivative of the second function.

Q: What values are given in the video to evaluate the derivative at x=3?

The video provides the values of the functions f and h, as well as their derivatives, at x=3: f(3)=6, h(3)=0, f'(3)=6, and h'(3)=4.

Q: What is the result of evaluating the derivative at x=3?

By substituting the given values into the derivative formula, the result is g'(3) = 24.

Summary & Key Takeaways

• The video discusses evaluating the derivative of the product of two functions at a specific value.

• The product rule is introduced as a useful tool for finding the derivative of the product of two functions.

• The video provides step-by-step instructions on how to apply the product rule to evaluate the derivative and demonstrates the process with specific function values.