Video Summary

The product rule is a fundamental concept in differential calculus used to find the derivative of a product of two or more functions. Instead of expanding the product before differentiation (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: d/dx[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, add the derivative of the second function multiplied by the first function. The rule extends to products of more than two functions, though the calculation becomes more involved. Mastering the product rule is crucial for solving various problems in physics, engineering, and other fields that involve rates of change. Understanding the underlying principle of how the rule handles the interplay of the derivatives of each function is key to its effective application. Many practice problems are essential to develop proficiency.