(d^2)/(dx^2)((y)(2xe^{x^2}-2))

解

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

8 e^{x^{2}} x^{3} y + 8 e^{x^{2}} x^{2} \frac{d y}{d x} + 2 e^{x^{2}} x \frac{d ^{2} y}{d x ^{2}} + 12 e^{x^{2}} x y - 2 \frac{d ^{2} y}{d x ^{2}} + 4 e^{x^{2}} \frac{d y}{d x}

解答ステップ

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

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

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

\frac{d}{d x} (\frac{d y}{d x} (2 x e^{x^{2}} - 2) + 2 (2 e^{x^{2}} x^{2} + e^{x^{2}}) y) = 8 e^{x^{2}} x^{3} y + 8 e^{x^{2}} x^{2} \frac{d y}{d x} + 2 e^{x^{2}} x \frac{d ^{2} y}{d x ^{2}} + 12 e^{x^{2}} x y - 2 \frac{d ^{2} y}{d x ^{2}} + 4 e^{x^{2}} \frac{d y}{d x}

= 8 e^{x^{2}} x^{3} y + 8 e^{x^{2}} x^{2} \frac{d y}{d x} + 2 e^{x^{2}} x \frac{d ^{2} y}{d x ^{2}} + 12 e^{x^{2}} x y - 2 \frac{d ^{2} y}{d x ^{2}} + 4 e^{x^{2}} \frac{d y}{d x}