(d^2)/(dx^2)((y)(y^3-xy))

解

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

- 2 x \frac{d y}{d x}^{2} - 2 x y \frac{d ^{2} y}{d x ^{2}} - 4 y \frac{d y}{d x} + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}

解答ステップ

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

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

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

\frac{d}{d x} (- 2 x y \frac{d y}{d x} + 4 y^{3} \frac{d y}{d x} - y^{2}) = - 2 x \frac{d y}{d x}^{2} - 2 x y \frac{d ^{2} y}{d x ^{2}} - 4 y \frac{d y}{d x} + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}

= - 2 x \frac{d y}{d x}^{2} - 2 x y \frac{d ^{2} y}{d x ^{2}} - 4 y \frac{d y}{d x} + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}