Answer
$$\frac{{dy}}{{dx}} = \frac{3}{{\sqrt {1 - 9{x^2}} }}$$
Work Step by Step
$$\eqalign{
& y = {\sin ^{ - 1}}\left( {3x} \right) \cr
& {\text{differentiate using the formula }} \cr
& \frac{d}{{dx}}\left[ {{{\sin }^{ - 1}}u} \right] = \frac{1}{{\sqrt {1 - {u^2}} }}\frac{{du}}{{dx}}{\text{ }}\left( {{\text{see page 467}}} \right) \cr
& \cr
& \frac{{dy}}{{dx}} = \frac{1}{{\sqrt {1 - {{\left( {3x} \right)}^2}} }}\frac{d}{{dx}}\left( {3x} \right) \cr
& \frac{{dy}}{{dx}} = \frac{1}{{\sqrt {1 - {{\left( {3x} \right)}^2}} }}\left( 3 \right) \cr
& {\text{simplifying}} \cr
& \frac{{dy}}{{dx}} = \frac{3}{{\sqrt {1 - 9{x^2}} }} \cr} $$
