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Occasionally, functions are written more succinctly than y = f(x), making it difficult or impossible to define y clearly in terms of x. Implicit functions are the name given to such functions; implicit differentiation may be used to distinguish them. It’s critical to do many practice activities to understand the concepts described here so that they become second nature. Implicit differentiation is commonly used across the business sector to solve various problems and optimize the output of the problem. In this post, I will discuss the application of Implicit Differentiation in the business sector.
In business, this approach entails differentiating an implicit equation concerning the desired variable while treating the remaining variables as undetermined functions known as implicit differentiation. Price and demand interactions are daily in practice as a spreadsheet of prices and sales, and various variables influence their changes (May & Bart, 2020). So these are the theoretical foundations that are used to discover in reality; in the economic literature, calculus (Implicit Differentiation) provides us with some pleasant ways to interpret the spreadsheet. Even if there is no solution for y directly, implicit differentiation assumes that y is a function of x. This assumption does not need any effort, but one must be extremely cautious when differentiating and utilizing the Chain Rule to consider y as a function.
Lastly, many business-based platforms are customized using implicit differential equations by software engineers. Algorithmic Adjoin Differentiation is a quick and easy approach to get price derivatives from input data. When a model calibration is conducted, it shows how the process can increase even further. Differentiating the numerical method utilized in calibration is not necessary when using the implicit function theorem. The outcome is a more practical application than automatic differentiation. Economists use this operation daily while software engineers develop complex platforms to solve the more challenging problem.
References
May, M., & Bart, A. (2020). Business Calculus with Excel. Mathstat.slu.edu. Web.
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