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

解

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

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

解答ステップ

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

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

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

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

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