(d^2)/(dx^2)((y)(4x^3-7x^2+3x-9))

解

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{3} - 7 x^{2} + 3 x - 9))

\frac{d ^{2} y}{d x ^{2}} (4 x^{3} - 7 x^{2} + 3 x - 9) + 2 (12 x^{2} - 14 x + 3) \frac{d y}{d x} + (24 x - 14) y

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{3} - 7 x^{2} + 3 x - 9))

\frac{d}{d x} (y (4 x^{3} - 7 x^{2} + 3 x - 9)) = \frac{d y}{d x} (4 x^{3} - 7 x^{2} + 3 x - 9) + (12 x^{2} - 14 x + 3) y

= \frac{d}{d x} (\frac{d y}{d x} (4 x^{3} - 7 x^{2} + 3 x - 9) + (12 x^{2} - 14 x + 3) y)

\frac{d}{d x} (\frac{d y}{d x} (4 x^{3} - 7 x^{2} + 3 x - 9) + (12 x^{2} - 14 x + 3) y) = \frac{d ^{2} y}{d x ^{2}} (4 x^{3} - 7 x^{2} + 3 x - 9) + 2 (12 x^{2} - 14 x + 3) \frac{d y}{d x} + (24 x - 14) y

= \frac{d ^{2} y}{d x ^{2}} (4 x^{3} - 7 x^{2} + 3 x - 9) + 2 (12 x^{2} - 14 x + 3) \frac{d y}{d x} + (24 x - 14) y