(d^2)/(dx^2)((y)((4x^2-1)^2))

解

\frac{d ^{2}}{d x ^{2}} ((y) ((4 x^{2} - 1)^{2}))

16 x^{4} \frac{d ^{2} y}{d x ^{2}} + 128 x^{3} \frac{d y}{d x} - 8 x^{2} \frac{d ^{2} y}{d x ^{2}} + 192 x^{2} y - 32 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 16 y

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) ((4 x^{2} - 1)^{2}))

\frac{d}{d x} (y (4 x^{2} - 1)^{2}) = \frac{d y}{d x} (4 x^{2} - 1)^{2} + 16 x (4 x^{2} - 1) y

= \frac{d}{d x} (\frac{d y}{d x} (4 x^{2} - 1)^{2} + 16 x (4 x^{2} - 1) y)

\frac{d}{d x} (\frac{d y}{d x} (4 x^{2} - 1)^{2} + 16 x (4 x^{2} - 1) y) = 16 x^{4} \frac{d ^{2} y}{d x ^{2}} + 128 x^{3} \frac{d y}{d x} - 8 x^{2} \frac{d ^{2} y}{d x ^{2}} + 192 x^{2} y - 32 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 16 y

= 16 x^{4} \frac{d ^{2} y}{d x ^{2}} + 128 x^{3} \frac{d y}{d x} - 8 x^{2} \frac{d ^{2} y}{d x ^{2}} + 192 x^{2} y - 32 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 16 y