Product Rule
The Product Rule is a fundamental principle in calculus used to find the derivative of a product of two functions. If you have two functions, f(x) and g(x), the Product Rule states that the derivative of their product, f(x) * g(x), is given by f'(x) * g(x) + f(x) * g'(x). This means you differentiate the first function and multiply it by the second function, then add the first function multiplied by the derivative of the second.
This rule is particularly useful in various fields, including physics and engineering, where products of functions frequently occur. By applying the Product Rule, you can simplify the process of finding derivatives, making it easier to analyze rates of change in complex systems. Understanding this rule is essential for anyone studying calculus or related disciplines.