(d^2)/(dx^2)((y)(12)(5x^2-1)(x^2-1))

解

\frac{d ^{2}}{d x ^{2}} ((y) (12) (5 x^{2} - 1) (x^{2} - 1))

12 (\frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 1) (x^{2} - 1) + 2 (20 x^{3} - 12 x) \frac{d y}{d x} + (60 x^{2} - 12) y)

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (12) (5 x^{2} - 1) (x^{2} - 1))

\frac{d}{d x} (y \cdot 12 (5 x^{2} - 1) (x^{2} - 1)) = 12 (\frac{d y}{d x} (5 x^{2} - 1) (x^{2} - 1) + (20 x^{3} - 12 x) y)

= \frac{d}{d x} (12 (\frac{d y}{d x} (5 x^{2} - 1) (x^{2} - 1) + (20 x^{3} - 12 x) y))

\frac{d}{d x} (12 (\frac{d y}{d x} (5 x^{2} - 1) (x^{2} - 1) + (20 x^{3} - 12 x) y)) = 12 (\frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 1) (x^{2} - 1) + 2 (20 x^{3} - 12 x) \frac{d y}{d x} + (60 x^{2} - 12) y)

= 12 (\frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 1) (x^{2} - 1) + 2 (20 x^{3} - 12 x) \frac{d y}{d x} + (60 x^{2} - 12) y)