(d^2)/(dx^2)((y)(4y+1))

解答

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

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

求解步骤

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

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

= \frac{d}{d x} (8 y \frac{d y}{d x} + \frac{d y}{d x})

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

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

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