## f'(g(x))g'(x)

### The expression f'(g(x))g'(x) represents the product of two derivatives: f'(g(x)) and g'(x)

The expression f'(g(x))g'(x) represents the product of two derivatives: f'(g(x)) and g'(x).

To understand this expression, let’s break it down into two parts:

1. f'(g(x)): This represents the derivative of the function f(x) evaluated at g(x). It means that you first find the derivative of f(x), and then substitute g(x) into that derivative. This is known as the chain rule in calculus. It is used when you have a composition of functions, where g(x) is inside the function f(x).

2. g'(x): This represents the derivative of the function g(x). It is the rate at which g(x) is changing with respect to x.

To find the derivative of a composite function, you can use the chain rule. The chain rule states that if we have a function h(x) = f(g(x)), then its derivative is given by:

h'(x) = f'(g(x)) * g'(x)

Here, h'(x) would be equivalent to f'(g(x))g'(x) in the given expression.

In summary, the expression f'(g(x))g'(x) represents the derivative of a composite function formed by the composition of f(x) and g(x).

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