Chapter 4 - Applications of the Derivative - 4.5 Linear Approximation and Differentials - 4.5 Exercises - Page 289: 43

$$dy = - \frac{3}{{{x^4}}}dx$$

$$\eqalign{ & f\left( x \right) = \frac{1}{{{x^3}}} \cr & f\left( x \right) = {x^{ - 3}} \cr & {\text{Differentiate}} \cr & f'\left( x \right) = \frac{d}{{dx}}\left[ {{x^{ - 3}}} \right] \cr & f'\left( x \right) = - 3{x^{ - 4}} \cr & or \cr & f'\left( x \right) = - \frac{3}{{{x^4}}} \cr & {\text{Write in the form }}dy = f'\left( x \right)dx \cr & dy = - \frac{3}{{{x^4}}}dx \cr} $$