Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3 - Page 140: 43

(a) $y''' = -210x^{-8} + 60x^{2}$ (b) $y'''= -6/x^{4}$ (c) $y''' = 6a$

(a) $y' = -5x^{-6} + 5x^{4}$ $\Rightarrow y'' = 30x^{-7} + 20x^{3}$ $\Rightarrow y''' = -210x^{-8} + 60x^{2}$ (b) $y = x^{-1}$ $\Rightarrow y' = -x^{-2}$ $\Rightarrow y'' = 2x^{-3}$ $\Rightarrow y''' = -6x^{-4}$ $= -6/x^{4}$ (c) $y' = 3ax^{2} + b$ $\Rightarrow y'' = 6ax$ $\Rightarrow y''' = 6a$