`g(x) = arcsin(3x)/x` Find the derivative of the function

The given function `g(x)` has a form `u(x)/v(x),` thus its derivative may be determined by the quotient rule:  `(u/v)' = (u' v - u v')/v^2.`

Also we need to know that the derivative of acrsine function is  `1/sqrt(1 - x^2),` and a bit of the chain rule.

The result of applying these rules is

`(arcsin(3x)/x)' = (x*(arcsin(3x))' - arcsin(3x))/x^2 = ((3x)/sqrt(1-9x^2) - arcsin(3x))/x^2,`

or it may be written as  `3/(x sqrt(1-9x^2)) - arcsin(3x)/x^2.`