$\frac{d}{dx} [\log(\cos x)]$

If $y = \log_{\sin x} (\tan x)$,then $\left( \frac{dy}{dx} \right)_{\pi/4}$ is equal to

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

The derivative of $(\sin x)^x$ with respect to $x^{(\sin x)}$ is

If $\phi(x) = \log_{5} \log_{3} x$,then $\phi'(e)$ is equal to

If $f(x)=3^x$ and $g(x)=4^x$,then $\frac{f^{\prime}(0)-g^{\prime}(0)}{1+f^{\prime}(0) g^{\prime}(0)}$ is