(d^2)/(dx^2)(-(2x^2)/(5y^2))

解

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

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

解答ステップ

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

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

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

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

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