(d^2)/(dx^2)((y)(x^4+y^4-16))

解

\frac{d ^{2}}{d x ^{2}} ((y) (x^{4} + y^{4} - 16))

x^{4} \frac{d ^{2} y}{d x ^{2}} + 8 x^{3} \frac{d y}{d x} + 12 x^{2} y + 20 y^{3} \frac{d y}{d x}^{2} + 5 y^{4} \frac{d ^{2} y}{d x ^{2}} - 16 \frac{d}{d x} (\frac{d y}{d x})

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (x^{4} + y^{4} - 16))

\frac{d}{d x} (y (x^{4} + y^{4} - 16)) = x^{4} \frac{d y}{d x} + 4 x^{3} y + 5 y^{4} \frac{d y}{d x} - 16 \frac{d y}{d x}

= \frac{d}{d x} (x^{4} \frac{d y}{d x} + 4 x^{3} y + 5 y^{4} \frac{d y}{d x} - 16 \frac{d y}{d x})

\frac{d}{d x} (x^{4} \frac{d y}{d x} + 4 x^{3} y + 5 y^{4} \frac{d y}{d x} - 16 \frac{d y}{d x}) = x^{4} \frac{d ^{2} y}{d x ^{2}} + 8 x^{3} \frac{d y}{d x} + 12 x^{2} y + 20 y^{3} \frac{d y}{d x}^{2} + 5 y^{4} \frac{d ^{2} y}{d x ^{2}} - 16 \frac{d}{d x} (\frac{d y}{d x})

= x^{4} \frac{d ^{2} y}{d x ^{2}} + 8 x^{3} \frac{d y}{d x} + 12 x^{2} y + 20 y^{3} \frac{d y}{d x}^{2} + 5 y^{4} \frac{d ^{2} y}{d x ^{2}} - 16 \frac{d}{d x} (\frac{d y}{d x})