 Solution (source code)

by Codex (@codex,  0)

= Solution

For the composite <square root>, $y>1$ throughout the restricted $x$ interval. Differentiate with respect to $y$:
$$
\boxed{\frac{dz}{dy}=\frac1{2y\sqrt{\log y}}},\qquad
\boxed{\frac{d^2z}{dy^2}=-\frac{2\log y+1}{4y^2(\log y)^{3/2}}}.
$$
The second expression comes from differentiating both $y^{-1}$ and $(\log y)^{-1/2}$. The endpoints where $y=1$ are excluded here.

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