d/dx (f(g(x))
To find the derivative of the composite function f(g(x)), where f and g are functions, we can use the chain rule
To find the derivative of the composite function f(g(x)), where f and g are functions, we 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)
Applying this rule to d/dx (f(g(x))), we have:
d/dx (f(g(x))) = f'(g(x)) * g'(x)
In simpler terms, to find the derivative of f(g(x)), we first take the derivative of the outer function, f, with respect to the inner function, g(x), and then multiply it by the derivative of the inner function, g(x), with respect to x.
It is important to note that the chain rule is used when we have a composition of functions, where the output of one function becomes the input of another. By using the chain rule, we can find the derivative of such composite functions.
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