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Find the instantaneous rate of change of f(x) = ln(x^2 + 4) at x = 3.

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Final answer:

The instantaneous rate of change of f(x) = ln(x^2 + 4) at x = 3 can be found by taking the derivative of the function and evaluating it at x = 3.

Step-by-step explanation:

The instantaneous rate of change of f(x) = ln(x^2 + 4) at x = 3 can be found using the derivative of the function. To find the derivative, we apply the chain rule. The derivative of ln(u) is 1/u times the derivative of u. In this case, u = x^2 + 4. So, the derivative of f(x) is 1/(x^2 + 4) times the derivative of (x^2 + 4), which is 2x. Evaluating the derivative at x = 3 gives us the instantaneous rate of change at that point.

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