(d^2)/(dx^2)((y)(4x^2+9y^2))

解

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{2} + 9 y^{2}))

4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 54 y \frac{d y}{d x}^{2} + 27 y^{2} \frac{d ^{2} y}{d x ^{2}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{2} + 9 y^{2}))

\frac{d}{d x} (y (4 x^{2} + 9 y^{2})) = 4 x^{2} \frac{d y}{d x} + 8 x y + 27 y^{2} \frac{d y}{d x}

= \frac{d}{d x} (4 x^{2} \frac{d y}{d x} + 8 x y + 27 y^{2} \frac{d y}{d x})

\frac{d}{d x} (4 x^{2} \frac{d y}{d x} + 8 x y + 27 y^{2} \frac{d y}{d x}) = 4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 54 y \frac{d y}{d x}^{2} + 27 y^{2} \frac{d ^{2} y}{d x ^{2}}

= 4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 54 y \frac{d y}{d x}^{2} + 27 y^{2} \frac{d ^{2} y}{d x ^{2}}