Chapter 4 - Applications of the Derivative - 4.5 Linear Approximation and Differentials - 4.5 Exercises - Page 289: 48

$$dy = \frac{1}{{\sqrt {1 - {x^2}} }}dx$$

$$\eqalign{ & f\left( x \right) = {\sin ^{ - 1}}x \cr & {\text{Differentiate }} \cr & f'\left( x \right) = \frac{d}{{dx}}\left[ {{{\sin }^{ - 1}}x} \right] \cr & f'\left( x \right) = \frac{1}{{\sqrt {1 - {x^2}} }} \cr & {\text{Write in the form }}dy = f'\left( x \right)dx \cr & dy = \frac{1}{{\sqrt {1 - {x^2}} }}dx \cr} $$