Question

Question:-
Explain the Chain rule or Function of a function rule. Give one or two examples.​

Answer 1

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.

is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².

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Answer 2

The chain rule-

The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².

What is the function of a function rule?

The function rule of a specific function, explains how to determine the value of the dependent variable say y, in terms of the independent variable say x. In simple words, a function rule is defined as the process that changes the input value to output.

Example 1: y = (1+ cos 2x)2

y' = 2( 1+ cos 2x) . (-sin 2x). (2)

= - 4(1+ cos 2x) . sin2x

Example 2: y = sin (cos (x2))

y' = cos(cos (x2)). -sin (x2)). 2x

= -2x sin (x2) cos (cos x2)

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