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

解

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

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

解答ステップ

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

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

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

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

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