# How do you differentiate x/ sqrt (x^2 +1)?

$\setminus \frac{1}{{\left({x}^{2} + 1\right)}^{\frac{3}{2}}}$

#### Explanation:

Differentiating given function: $\frac{x}{\setminus} \sqrt{{x}^{2} + 1}$ w.r.t. $x$ by using quotient rule as follows

$\frac{d}{\mathrm{dx}} \left(x \frac{\setminus}{\sqrt{{x}^{2} + 1}}\right)$

$= \setminus \frac{\setminus \sqrt{{x}^{2} + 1} \frac{d}{\mathrm{dx}} \left(x\right) - x \frac{d}{\mathrm{dx}} \setminus \sqrt{{x}^{2} + 1}}{{\left(\setminus \sqrt{{x}^{2} + 1}\right)}^{2}}$

$= \setminus \frac{\setminus \sqrt{{x}^{2} + 1} \left(1\right) - x \setminus \frac{2 x}{2 \setminus \sqrt{{x}^{2} + 1}}}{{\left(\setminus \sqrt{{x}^{2} + 1}\right)}^{2}}$

$= \setminus \frac{{x}^{2} + 1 - {x}^{2}}{\setminus \sqrt{{x}^{2} + 1} \left({x}^{2} + 1\right)}$

$= \setminus \frac{1}{{\left({x}^{2} + 1\right)}^{\frac{3}{2}}}$