(d^2)/(dx^2)((y)(4x-1))

解

\frac{d ^{2}}{d x ^{2}} ((y) (4 x - 1))

4 x \frac{d ^{2} y}{d x ^{2}} - \frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x}

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((y) (4 x - 1))

\frac{d}{d x} (y (4 x - 1)) = \frac{d y}{d x} (4 x - 1) + 4 y

= \frac{d}{d x} (\frac{d y}{d x} (4 x - 1) + 4 y)

\frac{d}{d x} (\frac{d y}{d x} (4 x - 1) + 4 y) = 4 x \frac{d ^{2} y}{d x ^{2}} - \frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x}

= 4 x \frac{d ^{2} y}{d x ^{2}} - \frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x}