If $y=\log \left[\mathrm{e}^{5 x}\left(\frac{3 x-4}{x+5}\right)^{\frac{4}{3}}\right]$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

Let $f$ be a twice differentiable function such that $\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x), \mathrm{f}^{\prime}(x)=\mathrm{g}(x)$ and $\mathrm{h}(x)=[\mathrm{f}(x)]^2+[\mathrm{g}(x)]^2$. If $\mathrm{h}(5)=1$, then $\mathrm{h}(10)$ is __________.

If $y=\sec \left(\tan ^{-1} x\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is equal to

If $\mathrm{f}(x)=\log _{x^2}\left(\log _{\mathrm{e}} x\right)$, then $\mathrm{f}^{\prime}(x)$ at $x=\mathrm{e}$ is