If you have a recursive function $$g(x) = f(f(x))$$ and you know that $$f(0) = 0, f'(0) = 1, f''(0) = 2$$ Will then $$g(0) = 0, g'(0) = 1, g''(0) = 2$$ ?
2026-03-28 14:37:05.1774708625
Recursive functions.
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Using the chain rule we can arrive at the fact that $$g'(x)=(f(f(x)))'=f'(f(x))f'(x)$$ Then using the product rule you can find the second derivative. Can you take it from here?