Chapter 4 - Applications of the Derivative - 4.5 Linear Approximation and Differentials - 4.5 Exercises - Page 289: 44

$$dy = 2{e^{2x}}dx$$

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