Video Summary

The product rule is a fundamental concept in calculus used to find the derivative of a function that is the product of two or more functions. Instead of expanding the product before differentiating (which can be cumbersome or impossible), the product rule provides a direct method. It states that the derivative of a product of two functions, f(x) and g(x), is given by: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x). This means you find the derivative of the first function, multiply it by the second function, then add the result of the first function multiplied by the derivative of the second function. The product rule extends to more than two functions, though the number of terms increases with each additional function. Mastering the product rule is crucial for solving a wide range of problems in calculus, including finding slopes of tangent lines, optimization problems, and related rates problems. Understanding how to apply the rule correctly is essential for accurate calculations and problem-solving.