Lagrange Inversion Formula

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Is there any simple way to prove the Taylor's Expansion Formula of inverse functions ? How Lagrange Inversion Formula can be proven ? Is there any easy way to make it ?

thank you

Since if f(a) = b then f^(-1)(b) = a, it is easy to understand the differences between normal and inverse expansions but I couldn't find a way to show where the coefficient (which contains limit and derivative inside) come from ?

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