Answer
$$\frac{3}{{\sqrt x }}\left[ {\csc \left( {1 - 2\sqrt x } \right)\cot \left( {1 - 2\sqrt x } \right)} \right]dx$$
Work Step by Step
$$\eqalign{
& y = 3\csc \left( {1 - 2\sqrt x } \right) \cr
& {\text{Differentiate with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {3\csc \left( {1 - 2\sqrt x } \right)} \right] \cr
& {\text{Recall that }}\frac{d}{{dx}}\left[ {\csc u} \right] = - \csc u\cot u\frac{{du}}{{dx}} \cr
& \frac{{dy}}{{dx}} = - 3\csc \left( {1 - 2\sqrt x } \right)\cot \left( {1 - 2\sqrt x } \right)\frac{d}{{dx}}\left[ {1 - 2\sqrt x } \right] \cr
& \frac{{dy}}{{dx}} = - 3\csc \left( {1 - 2\sqrt x } \right)\cot \left( {1 - 2\sqrt x } \right)\left( { - \frac{2}{{2\sqrt x }}} \right) \cr
& \frac{{dy}}{{dx}} = - 3\csc \left( {1 - 2\sqrt x } \right)\cot \left( {1 - 2\sqrt x } \right)\left( { - \frac{1}{{\sqrt x }}} \right) \cr
& \frac{{dy}}{{dx}} = \frac{{3\csc \left( {1 - 2\sqrt x } \right)\cot \left( {1 - 2\sqrt x } \right)}}{{\sqrt x }} \cr
& {\text{Write in differential form}} \cr
& dy = \frac{3}{{\sqrt x }}\left[ {\csc \left( {1 - 2\sqrt x } \right)\cot \left( {1 - 2\sqrt x } \right)} \right]dx \cr} $$
