What is the triple product rule?


Quick Answer

The triple product rule is essentially a generalization of the product rule in calculus. The product rule is a formula used to find the derivatives of two or more functions. The triple product rule follows the same operation as the product rule, but applied in multiple steps.

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Full Answer

According to TutorVista, the product rule serves as a way to differentiate functions that are being multiplied by one another. When two functions are multiplied together, the product's derivative equals the first function multiplied by the derivative of the second, added to the second function multiplied by the derivative of the first function.

Product rules and derivatives can be difficult to analyze and prove, but the triple product rule makes finding solutions a bit easier. Using the triple product rule, it is possible to find the quotients of partial derivatives, which are easier to work with than the partial derivatives themselves. The quotients can then be used to find an equation solution through the process of substitution.

The triple product rule is frequently used in thermodynamics, where three variables grouped together are often found to be interdependent. The triple product rule is also known as Euler's chain rule, the cyclical rule and cyclic relation.

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