Answer
$$dy = - \frac{x}{{\sqrt {36 - {x^2}} }}dx$$
Work Step by Step
$$\eqalign{
& y = \sqrt {36 - {x^2}} \cr
& y = {\left( {36 - {x^2}} \right)^{1/2}} \cr
& {\text{Differentiate both sides with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {{{\left( {36 - {x^2}} \right)}^{1/2}}} \right] \cr
& \frac{{dy}}{{dx}} = \frac{1}{2}{\left( {36 - {x^2}} \right)^{ - 1/2}}\frac{d}{{dx}}\left[ {36 - {x^2}} \right] \cr
& \frac{{dy}}{{dx}} = \frac{1}{2}{\left( {36 - {x^2}} \right)^{ - 1/2}}\left( { - 2x} \right) \cr
& \frac{{dy}}{{dx}} = {\left( {36 - {x^2}} \right)^{ - 1/2}}\left( { - x} \right) \cr
& \frac{{dy}}{{dx}} = - \frac{x}{{\sqrt {36 - {x^2}} }} \cr
& {\text{Write in differential form }}dy = f'\left( x \right)dx \cr
& dy = - \frac{x}{{\sqrt {36 - {x^2}} }}dx \cr} $$
