If $y = \log_3(\log_3 x)$,then $\frac{dy}{dx}$ at $x = 3$ is $\ldots \ldots$

If $y=\log \sqrt{\frac{1+\sin x}{1-\sin x}}$,then $\frac{d y}{d x}$ at $x=\frac{\pi}{3}$ is

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

Let $\ln x$ denote the logarithm of $x$ with respect to the base $e$. Let $S \subset R$ be the set of all points where the function $\ln(x^2-1)$ is well-defined. Then,the number of functions $f: S \rightarrow R$ that are differentiable,satisfy $f^{\prime}(x)=\ln(x^2-1)$ for all $x \in S$ and $f(2)=0$,is

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

$\frac{d}{dx} \left[ \log \left\{ e^x \left( \frac{x + 2}{x - 2} \right)^{3/4} \right\} \right]$ equals