Derivatives, in mathematics, the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations. In general, scientists observe changing systems to obtain the rate of change of some variable of interest, incorporate this information into some differential equation, and use integration techniques to obtain a function that can be used to predict the behavior of the original system under diverse conditions.
Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. The derivative is often written using “dy over dx” (meaning the difference in y divided by the difference in x). Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.
The slope is often expressed as the “rise” over the “run,” or, in Cartesian terms, the ratio of the change in y to the change in x. We always use the concept of derivatives in our professional and daily lives, a couple of such examples are:
Uses of Derivatives
Derivatives provide three important economic functions: (1) risk management, (2) price discovery, and (3) transactional efficiency. The primary purpose of risk management is to protect existing profits, not to create new profits.
Derivatives can be used in risk management to hedge a position, protecting against the risk of an adverse move in an asset. Hedging is the act of taking an offsetting position in a related security, which helps to mitigate against opposite price movements.
In business, we come across many such variables where one variable is a function of the other. For example, the quantity demanded can be said to be a function of price. Supply and price or cost and quantity demanded are some other such variables.
Derivatives help us in finding the rate at which one such quantity changes with respect to the other. Marginal analysis in Economics and Commerce is the most direct application of differential calculus.
Derivatives are constantly used in everyday life to help measure how much something is changing. They are used by the Govt. in the population census, various types of sciences, and even in econometrics as we’ve seen above. Knowing how to use derivatives, when to use them and their application in our lives can be a crucial part of any profession, so learning it well can be said to be highly beneficial.
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