![]() It is used to calculate derivatives of different functions like, trigonometric, hyperbolic, exponential etc. The chain rule of derivative is a method of finding rate of change of a function with respect to another function, if the function is in a composition form. du / dx = derivative of u with respect to x.dy / du = derivative of y with respect to u.dy / dx = derivative of y with respect to x. ![]() Determine intervals on which f(x) 2x3 3x236x+2 is increasing or decreasing. Increasing/Decreasing If f(x) >0 on an interval I, then f(x) is increasing on I, and if f(x) <0 on an interval I, then f(x) is decreasing on I. Substitute u = g(x) then we can write above function as: To determine where a function is increasing or decreasing, we use the derivative as in the following theorem. Suppose that we have two functions f(x) and g(x) then the function of f as the function g can be written as: The product rule is differentiating a function that formed by the product of two different functions. It is because other differentiation rules are not applicable for a complex or combination of two functions. The chain is applicable for finding derivatives of composite functions only. It helps to evaluate the differentiation of a function that can be expressed as a function of another or a function formed by combining two functions. The Extreme Value Theorem In this section we will solve the problem of finding the maximum and minimum values of a continuous function on a closed interval. It is a method of finding the derivative of a function that is a function of another function. Extreme Value Theorem In this section we learn the Extreme Value Theorem and we find the extremes of a function. This article will help you to learn more about chain rule and its applications. This principle is often used to calculate derivatives of complicated functions. The chain rule is a mathematical principle that states that a derivative of a function can be found by applying the derivative of the function to each of the derivatives of the functions that are involved in the chain. ![]() What is the Chain Rule in Calculus? Introduction
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