(d^2)/(dx^2)((y)(5x^2+y^4-21))

解

\frac{d ^{2}}{d x ^{2}} ((y) (5 x^{2} + y^{4} - 21))

5 x^{2} \frac{d ^{2} y}{d x ^{2}} + 20 x \frac{d y}{d x} + 10 y + 20 y^{3} \frac{d y}{d x}^{2} + 5 y^{4} \frac{d ^{2} y}{d x ^{2}} - 21 \frac{d}{d x} (\frac{d y}{d x})

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (5 x^{2} + y^{4} - 21))

\frac{d}{d x} (y (5 x^{2} + y^{4} - 21)) = 5 x^{2} \frac{d y}{d x} + 10 x y + 5 y^{4} \frac{d y}{d x} - 21 \frac{d y}{d x}

= \frac{d}{d x} (5 x^{2} \frac{d y}{d x} + 10 x y + 5 y^{4} \frac{d y}{d x} - 21 \frac{d y}{d x})

\frac{d}{d x} (5 x^{2} \frac{d y}{d x} + 10 x y + 5 y^{4} \frac{d y}{d x} - 21 \frac{d y}{d x}) = 5 x^{2} \frac{d ^{2} y}{d x ^{2}} + 20 x \frac{d y}{d x} + 10 y + 20 y^{3} \frac{d y}{d x}^{2} + 5 y^{4} \frac{d ^{2} y}{d x ^{2}} - 21 \frac{d}{d x} (\frac{d y}{d x})

= 5 x^{2} \frac{d ^{2} y}{d x ^{2}} + 20 x \frac{d y}{d x} + 10 y + 20 y^{3} \frac{d y}{d x}^{2} + 5 y^{4} \frac{d ^{2} y}{d x ^{2}} - 21 \frac{d}{d x} (\frac{d y}{d x})