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F(g(x))

Series expansion at x = 0

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

Derivative

d/dx(f(g(x))) = g'(x) f'(g(x))

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