(d^2)/(dx^2)((y)(x^2-1)^3)

解

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} - 1)^{3})

\frac{d ^{2} y}{d x ^{2}} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} \frac{d y}{d x} + 6 (x^{5} \frac{d y}{d x} + 5 x^{4} y - 2 x^{3} \frac{d y}{d x} - 6 x^{2} y + x \frac{d y}{d x} + y)

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} - 1)^{3})

\frac{d}{d x} (y (x^{2} - 1)^{3}) = \frac{d y}{d x} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} y

= \frac{d}{d x} (\frac{d y}{d x} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} y)

\frac{d}{d x} (\frac{d y}{d x} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} y) = \frac{d ^{2} y}{d x ^{2}} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} \frac{d y}{d x} + 6 (x^{5} \frac{d y}{d x} + 5 x^{4} y - 2 x^{3} \frac{d y}{d x} - 6 x^{2} y + x \frac{d y}{d x} + y)

= \frac{d ^{2} y}{d x ^{2}} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} \frac{d y}{d x} + 6 (x^{5} \frac{d y}{d x} + 5 x^{4} y - 2 x^{3} \frac{d y}{d x} - 6 x^{2} y + x \frac{d y}{d x} + y)