Leibniz Formula
The Leibniz Formula refers to a mathematical expression that provides a way to compute the derivative of a product of two functions. Named after the mathematician Gottfried Wilhelm Leibniz, this formula states that the derivative of the product of two functions, f(x) and g(x), is given by the formula: (f \cdot g)' = f' \cdot g + f \cdot g' . This principle is fundamental in calculus and is widely used in various applications.
In addition to its application in derivatives, the Leibniz Formula also extends to the computation of higher-order derivatives. The formula can be generalized to express the n -th derivative of a product of functions, which is useful in advanced calculus and mathematical analysis. Understanding this formula is essential for students and professionals working in fields that involve calculus, such as physics, engineering, and economics.