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

解

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

x^{3} \frac{d ^{2} y}{d x ^{2}} + 6 x^{2} \frac{d y}{d x} + 6 x y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}

解答ステップ

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

\frac{d}{d x} (y (x^{3} + y^{3})) = x^{3} \frac{d y}{d x} + 3 x^{2} y + 4 y^{3} \frac{d y}{d x}

= \frac{d}{d x} (x^{3} \frac{d y}{d x} + 3 x^{2} y + 4 y^{3} \frac{d y}{d x})

\frac{d}{d x} (x^{3} \frac{d y}{d x} + 3 x^{2} y + 4 y^{3} \frac{d y}{d x}) = x^{3} \frac{d ^{2} y}{d x ^{2}} + 6 x^{2} \frac{d y}{d x} + 6 x y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}

= x^{3} \frac{d ^{2} y}{d x ^{2}} + 6 x^{2} \frac{d y}{d x} + 6 x y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}