Final answer:
The derivative of the composite function f(g(x)), with f(x) = x² - 4, is found using the chain rule to be 2g(x) · g'(x).
Step-by-step explanation:
To find the derivative of the composite function f(g(x)), where f(x) = x² - 4, we apply the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. For the given f(x), the outer function derivative is 2x, evaluated at g(x), which gives us 2g(x).
Now, if g is a differentiable function of x, we will denote its derivative as g'(x). Applying the chain rule, the derivative of f(g(x)) is 2g(x) multiplied by g'(x), which provides us with the final result:
f'(g(x)) = 2g(x) · g'(x).