泰勒 5/(x^3),-1

解答

泰勒

\frac{5}{x ^{3}}, - 1

- 5 - 15 (x + 1) - 30 (x + 1)^{2} - 50 (x + 1)^{3} - 75 (x + 1)^{4} + \dots

求解步骤

应用泰勒公式

= - 5 + \frac{\frac{d}{d x} ( \frac{5}{x ^{3}} ) ( - 1 )}{1 !} (x + 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{5}{x ^{3}} ) ( - 1 )}{2 !} (x + 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{5}{x ^{3}} ) ( - 1 )}{3 !} (x + 1)^{3} + \dots

求导数

= - 5 + \frac{- 15}{1 !} (x + 1) + \frac{- 60}{2 !} (x + 1)^{2} + \frac{- 300}{3 !} (x + 1)^{3} + \frac{- 1800}{4 !} (x + 1)^{4} + \dots

整理后得

= - 5 - 15 (x + 1) - 30 (x + 1)^{2} - 50 (x + 1)^{3} - 75 (x + 1)^{4} + \dots

\frac{\partial}{\partial x} (- 2 y cos (6 x))

\frac{\partial}{\partial y} (\frac{1}{x ^{2}} + \frac{1}{y ^{2}})

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\frac{d}{d x} (\frac{2}{1 - 2 x})

\frac{\partial}{\partial x} (\frac{x}{2 x ^{2} + y ^{2}})