The Chain Rule: Computing Derivatives Of Composite Functions With F'(G(X))G'(X)

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

chain rule

The expression f'(g(x))g'(x) represents the derivative of the composite function f(g(x)) with respect to x.

To compute the derivative of a composite function, we need to use the chain rule. The chain rule states that the derivative of a composite function can be obtained by multiplying the derivative of the outer function evaluated at the inner function, with the derivative of the inner function with respect to the independent variable.

In this case, let’s assume that f(x) is our outer function and g(x) is our inner function. Then we can apply the chain rule as follows:

f'(g(x))g'(x) = d/dx[f(g(x))] = f'(g(x))dg(x)/dx

Here, f'(g(x)) is the derivative of the outer function f(x) evaluated at the inner function g(x), and dg(x)/dx is the derivative of the inner function g(x) with respect to x.

Therefore, the expression f'(g(x))g'(x) represents the product of the derivative of the outer function with respect to the inner function evaluated at the argument g(x), and the derivative of the inner function with respect to x.

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