Chapter 4 - Applications of the Derivative - 4.5 Linear Approximation and Differentials - 4.5 Exercises - Page 289: 42

$$dy = \sin 2xdx$$

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