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F of G

Series expansion at g = 0

f(0) + g f'(0) + 1/2 g^2 f''(0) + 1/6 f^(3)(0) g^3 + 1/24 f^(4)(0) g^4 + O(g^5)
(Taylor series)

Derivative

d/dg(f(g)) = f'(g)

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