Chapter 7: Transcendental Functions - Section 7.4 - Exponential Change and Separable Differential Equations - Exercises 7.4 - Page 400: 2

a) $\dfrac{1}{x^2}$ b) $\dfrac{1}{(x+3)^2}$ c) $\dfrac{1}{(x+C)^2}$

a) Consider $y^2=\dfrac{1}{x^2}$ Then, $y'=-[(-1) (x^{-2})]=\dfrac{1}{x^2}$ b) Consider $y^2=\dfrac{1}{(x+3)^2}$ Then, $y'=-[(-1)( (x+3)^{-2})]=\dfrac{1}{(x+3)^2}$ c) Consider $y^2=\dfrac{1}{(x+C)^2}$ Then, $y'=-[(-1)] [(x+C)^{-2}]=\dfrac{1}{(x+C)^2}$