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

解

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

2 x^{3} \frac{d ^{2} y}{d x ^{2}} + 12 x^{2} \frac{d y}{d x} + 12 x y + 2 \frac{d y}{d x}^{2} + 2 y \frac{d ^{2} y}{d x ^{2}} + 6 y \frac{d y}{d x}^{2} + 3 y^{2} \frac{d ^{2} y}{d x ^{2}}

解答ステップ

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

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

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

\frac{d}{d x} (2 x^{3} \frac{d y}{d x} + 6 x^{2} y + 2 y \frac{d y}{d x} + 3 y^{2} \frac{d y}{d x}) = 2 x^{3} \frac{d ^{2} y}{d x ^{2}} + 12 x^{2} \frac{d y}{d x} + 12 x y + 2 \frac{d y}{d x}^{2} + 2 y \frac{d ^{2} y}{d x ^{2}} + 6 y \frac{d y}{d x}^{2} + 3 y^{2} \frac{d ^{2} y}{d x ^{2}}

= 2 x^{3} \frac{d ^{2} y}{d x ^{2}} + 12 x^{2} \frac{d y}{d x} + 12 x y + 2 \frac{d y}{d x}^{2} + 2 y \frac{d ^{2} y}{d x ^{2}} + 6 y \frac{d y}{d x}^{2} + 3 y^{2} \frac{d ^{2} y}{d x ^{2}}