d/dx f(g(x))
The expression “d/dx f(g(x))” represents the derivative of the composition of two functions, f(x) and g(x), with respect to the independent variable x
The expression “d/dx f(g(x))” represents the derivative of the composition of two functions, f(x) and g(x), with respect to the independent variable x. In other words, it is the derivative of the function f(g(x)).
To find this derivative, you need to apply the chain rule. The chain rule states that if y = f(g(x)), where f(u) is a function and g(x) is another function, then the derivative of y with respect to x can be computed as follows:
dy/dx = (dy/du) * (du/dx)
In this case, y = f(g(x)), so we need to find dy/dx. Using the chain rule, we have:
dy/dx = (dy/du) * (du/dx)
Let’s break it down:
(1) Find dy/du: Take the derivative of f(u) with respect to u, assuming u = g(x).
(2) Find du/dx: Take the derivative of g(x) with respect to x.
Once you have both (1) and (2), you can multiply them to find dy/dx, which represents the derivative of f(g(x)) with respect to x.
Note: It is important to know the specific functions f(x) and g(x) in order to perform the necessary differentiation.
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