If $y = \log_{2026}(\log_{2025} x)$,then $\frac{dy}{dx} = \dots \dots \dots$

$\frac{d}{dx} \left( \log \left( \sqrt{x + \sqrt{x^2 + a^2}} \right) \right) = $

If $y = \log^n x$,where $\log^n$ denotes the $n$-th iterated logarithm $\log_e(\log_e(\dots \log_e x \dots))$ ($n$ times),then $x \log x \log^2 x \log^3 x \dots \log^{n-1} x \log^n x \frac{dy}{dx}$ is equal to

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

$m$ is the slope of a tangent to the curve $e^{y}=1+x^2$ at $x=1$,then $m=$

The derivative of $\log _{e^2}(\log x)$ with respect to $x$ is $ . . . . . . $.