$$y=(1+x)\left(1+x^2\right)\left(1+x^4\right) \ldots \ldots \ldots\left(1+x^{2 n}\right)$$, then the value of $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=0$$ is

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

$$\text { For all real } x \text {, the minimum value of } \frac{1-x+x^2}{1+x+x^2} \text { is }$$

The set of all points, where the derivative of the functions $$\mathrm{f}(x)=\frac{x}{1+|x|}$$ exists, is