2016 is absolutely awesome 5

Calculus Level 5

Let \(f_1(x) = f(x) = \dfrac{9}{3+2x}\).

Then for \(n > 1\), let \(f_n(x) = f(f_{n−1}(x))\).

Find 3 last digits of \(f_{2016}^{\,'}(-3)\).


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