কোন ব্যবধিতে $f(x)=\frac{x}{x^{2}+1}$ ক্রমবর্ধমান?

$f(x)=\frac{x}{x^{2}+1}$ $\Rightarrow f^{\prime}(x)=\frac{\left(x^{2}+1\right) \times 1-x \times 2 x}{\left(x^{2}+1\right)^{2}}$ $=\frac{1-x^{2}}{\left(x^{2}+1\right)^{2}}$ ক্রমবর্ধমান ফাংশনের জন্য $f'(x) > 0$ $\Rightarrow \frac{1-x^{2}}{\left(x^{2}+1\right)^{2}}>0$ $\Rightarrow 1-x^{2}>0$ $\Rightarrow x^{2}-1<0$ $\Rightarrow x^{2}<1 \Rightarrow|x|^{2}<1$ $\Rightarrow|\mathrm{x}|<1$ $\therefore-1<\mathrm{x}<1$ $\therefore$ ব্যবধি $= (-1, 1)$