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alech4466
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I just learned about chain rule in calculus, but I was wondering why exactly chain rule works. I understand how to use it, just not exactly why it works.
Thanks in advance
Thanks in advance
The chain rule is a mathematical rule used in calculus that helps us find the derivative of a composite function. It is important because it allows us to solve complex functions by breaking them down into simpler parts.
The chain rule states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function. In other words, we take the derivative of the outer function and plug in the inner function, then multiply it by the derivative of the inner function.
The chain rule is necessary because without it, we would not be able to find the derivative of composite functions. It allows us to solve more complex functions and is an essential tool in calculus.
Sure! Let's say we have the function f(x) = (2x+1)^3. Using the chain rule, we can break this down into the outer function g(x) = x^3 and the inner function h(x) = 2x+1. The derivative of g(x) is 3x^2, and the derivative of h(x) is 2. Therefore, the derivative of f(x) is (3x^2)(2) = 6x^2.
One way to remember the chain rule is by using the acronym "UDU," which stands for "undo, derivative, undo." This reminds us to take the derivative of the outer function, then plug in the inner function, and finally multiply it by the derivative of the inner function.