If $y=2^{\log x}$,then $\frac{d y}{d x}$ is

If $y = \log \left(\frac{1-x^{2}}{1+x^{2}}\right)$,then $\frac{dy}{dx}$ is equal to

If $\frac{d}{dx} \left( A \log \left( \frac{\sqrt{1-x^3}-1}{\sqrt{1-x^3}+1} \right) \right) = \frac{1}{x \sqrt{1-x^3}}$,then $AB=$

$\frac{d}{dx}(e^{x \log x} + e^3) = $ . . . . . .

Find the derivative: $\frac{d}{dx} \log (\sqrt{x - a} + \sqrt{x - b})$

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