Explain chain rule with example.
Answers
Answer:
The chain rule is a method for finding the derivative of composite functions, or functions that are made by combining one or more functions. An example of one of these types of functions is f(x)=(1+x)2 which is formed by taking the function 1+x and plugging it into the function x2. A surprising number of functions can be thought of as composite and the chain rule can be applied to all of them.
Example
Find the derivative of f(x)=(3x+1)5.
Solution
In this example, there is a function 3x+1 that is being taken to the 5th power. So, there are two pieces: the 3x+1 (the inside function) and taking that to the 5th power (the outside function). You know by the power rule, that the derivative of x5 is 5x4. So, cover up that 3x+1, and pretend it is an x for a minute. The only deal is, you will have to pay a penalty. Since it was actually not just an x, you will have to multiply by the derivative of the 3x+1.
Step-by-step explanation:
The chain rule is a method for finding the derivative of composite functions, or functions that are made by combining one or more functions. An example of one of these types of functions is f(x)=(1+x)2 which is formed by taking the function 1+x and plugging it into the function x2.