Final answer:
The instantaneous rate of change of f(x)=ln(x²+5) at x=2 is 4/9.
Step-by-step explanation:
The instantaneous rate of change of the function f(x) = ln(x² + 5) at x = 2 can be found by taking the derivative of the function and evaluating it at x = 2. The derivative of the natural logarithm function is given by f'(x) = 2x / (x² + 5). Substitute x = 2 into the derivative function to get the instantaneous rate of change at that point: f'(2) = 2(2) / (2² + 5) = 4 / 9.