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

解

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

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

解答ステップ

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

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

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

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

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