(d^2)/(dx^2)((y)(2x^{5/3}-5x^{4/3}))

解

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}))

\frac{- 120 x \frac{d y}{d x} + 60 x ^{\frac{4}{3}} \frac{d y}{d x} + 20 x ^{\frac{1}{3}} y - 20 y + 18 x ^{\frac{7}{3}} \frac{d ^{2} y}{d x ^{2}} - 45 x ^{2} \frac{d ^{2} y}{d x ^{2}}}{9 x ^{\frac{2}{3}}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}))

\frac{d}{d x} (y (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}})) = \frac{d y}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}) + \frac{( 10 x ^{\frac{2}{3}} - 20 x ^{\frac{1}{3}} ) y}{3}

= \frac{d}{d x} \frac{d y}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}) + \frac{( 10 x ^{\frac{2}{3}} - 20 x ^{\frac{1}{3}} ) y}{3}

\frac{d}{d x} \frac{d y}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}) + \frac{( 10 x ^{\frac{2}{3}} - 20 x ^{\frac{1}{3}} ) y}{3} = \frac{- 120 x \frac{d y}{d x} + 60 x ^{\frac{4}{3}} \frac{d y}{d x} + 20 x ^{\frac{1}{3}} y - 20 y + 18 x ^{\frac{7}{3}} \frac{d ^{2} y}{d x ^{2}} - 45 x ^{2} \frac{d ^{2} y}{d x ^{2}}}{9 x ^{\frac{2}{3}}}

= \frac{- 120 x \frac{d y}{d x} + 60 x ^{\frac{4}{3}} \frac{d y}{d x} + 20 x ^{\frac{1}{3}} y - 20 y + 18 x ^{\frac{7}{3}} \frac{d ^{2} y}{d x ^{2}} - 45 x ^{2} \frac{d ^{2} y}{d x ^{2}}}{9 x ^{\frac{2}{3}}}