Understanding the Chain Rule | Derivative of a Composite Function

d/dx (f(g(x))

The expression d/dx (f(g(x))) represents the derivative of the composite function f(g(x)) with respect to x

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

To find this derivative, we can use the chain rule from calculus, which states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

Let’s break down the steps to find the derivative of f(g(x)):

1. Start with the function f(g(x)). Differentiate f(g(x)) with respect to x.
2. Apply the chain rule by differentiating the outer function f'(g(x)) and multiply it by the derivative of the inner function g'(x).

So, the derivative of f(g(x)) with respect to x can be computed as follows:

d/dx (f(g(x))) = f'(g(x)) * g'(x)

It is important to note that the functions f and g need to be differentiable in order to apply the chain rule and compute this derivative.

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