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