# What is the derivative of  (arcsin(3x))/x?

$f ' \left(x\right) = \setminus \frac{3 x - \setminus {\sin}^{- 1} \left(3 x\right) \setminus \sqrt{1 - 9 {x}^{2}}}{{x}^{2} \setminus \sqrt{1 - 9 {x}^{2}}}$

#### Explanation:

Given function

$f \left(x\right) = \setminus \frac{\setminus {\sin}^{- 1} \left(3 x\right)}{x}$

Using division rule, the derivative of given function

$f ' \left(x\right) = \setminus \frac{d}{\mathrm{dx}} \left(\setminus \frac{\setminus {\sin}^{- 1} \left(3 x\right)}{x}\right)$

$= \setminus \frac{x \setminus \frac{d}{\mathrm{dx}} \left(\setminus {\sin}^{- 1} \left(3 x\right)\right) - \setminus {\sin}^{- 1} \left(3 x\right) \setminus \frac{d}{\mathrm{dx}} x}{{x}^{2}}$

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

$= \setminus \frac{\setminus \frac{3 x}{\setminus \sqrt{1 - 9 {x}^{2}}} - \setminus {\sin}^{- 1} \left(3 x\right)}{{x}^{2}}$

$= \setminus \frac{3 x - \setminus {\sin}^{- 1} \left(3 x\right) \setminus \sqrt{1 - 9 {x}^{2}}}{{x}^{2} \setminus \sqrt{1 - 9 {x}^{2}}}$