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

解答

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

9 x^{4} \frac{d ^{2} y}{d x ^{2}} + 72 x^{3} \frac{d y}{d x} - 6 x^{2} \frac{d ^{2} y}{d x ^{2}} + 108 x^{2} y - 24 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 12 y

求解步骤

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

\frac{d}{d x} (y (3 x^{2} - 1)^{2}) = \frac{d y}{d x} (3 x^{2} - 1)^{2} + 12 x (3 x^{2} - 1) y

= \frac{d}{d x} (\frac{d y}{d x} (3 x^{2} - 1)^{2} + 12 x (3 x^{2} - 1) y)

\frac{d}{d x} (\frac{d y}{d x} (3 x^{2} - 1)^{2} + 12 x (3 x^{2} - 1) y) = 9 x^{4} \frac{d ^{2} y}{d x ^{2}} + 72 x^{3} \frac{d y}{d x} - 6 x^{2} \frac{d ^{2} y}{d x ^{2}} + 108 x^{2} y - 24 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 12 y

= 9 x^{4} \frac{d ^{2} y}{d x ^{2}} + 72 x^{3} \frac{d y}{d x} - 6 x^{2} \frac{d ^{2} y}{d x ^{2}} + 108 x^{2} y - 24 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 12 y

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