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

解

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

- 2 x \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 20 y^{3} \frac{d y}{d x}^{2} + 5 y^{4} \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d ^{2} y}{d x ^{2}}

解答ステップ

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

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

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

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

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