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The derivative of the indirect function f[g(x)] is
$\{f[g(x)]\}' = f'[g(x)]g'(x)$. For the second derivative of the product
of $f(x)$ and $g(x)$ one has 
$[f(x)g(x)]'' = f''(x)g(x) + 2f'(x)g'(x) + f(x)g''(x)$.
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