If $\mathrm{f}(x)=\log _{x^2}(\log x)$, then at $x=\mathrm{e}, \mathrm{f}^{\prime}(x)$ has the value

Let $\mathrm{f}(x)=\frac{x}{\sqrt{\mathrm{a}^2+x^2}}-\frac{\mathrm{d}-x}{\sqrt{\mathrm{~b}^2+(\mathrm{d}-x)^2}}, x \in \mathbb{R}$ where $\mathrm{a}, \mathrm{b}, \mathrm{d}$ are non-zero real constants. Then

If $y=(\sin x)^{\tan x}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

If $\mathrm{f}(x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)$, then $f^{\prime}(1)=$