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

解

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

- 4 x^{5} \frac{d ^{2} y}{d x ^{2}} - 40 x^{4} \frac{d y}{d x} - 80 x^{3} y + 4 \frac{d ^{2} y}{d x ^{2}}

解答ステップ

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

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

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

\frac{d}{d x} (\frac{d y}{d x} (- 4 x^{5} + 4) - 20 x^{4} y) = - 4 x^{5} \frac{d ^{2} y}{d x ^{2}} - 40 x^{4} \frac{d y}{d x} - 80 x^{3} y + 4 \frac{d ^{2} y}{d x ^{2}}

= - 4 x^{5} \frac{d ^{2} y}{d x ^{2}} - 40 x^{4} \frac{d y}{d x} - 80 x^{3} y + 4 \frac{d ^{2} y}{d x ^{2}}