Chapter 4 - Applications of the Derivative - 4.5 Linear Approximation and Differentials - 4.5 Exercises - Page 289: 49

$$dy = {\sec ^2}xdx$$

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