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

解答

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

- 2 x^{4} \frac{d ^{2} y}{d x ^{2}} - 16 x^{3} \frac{d y}{d x} - 24 x^{2} y + 5 x \frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 2 \frac{d y}{d x}^{2} + 2 y \frac{d ^{2} y}{d x ^{2}}

求解步骤

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

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

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

\frac{d}{d x} (- 2 x^{4} \frac{d y}{d x} - 8 x^{3} y + 5 x \frac{d y}{d x} + 2 y \frac{d y}{d x} + 5 y) = - 2 x^{4} \frac{d ^{2} y}{d x ^{2}} - 16 x^{3} \frac{d y}{d x} - 24 x^{2} y + 5 x \frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 2 \frac{d y}{d x}^{2} + 2 y \frac{d ^{2} y}{d x ^{2}}

= - 2 x^{4} \frac{d ^{2} y}{d x ^{2}} - 16 x^{3} \frac{d y}{d x} - 24 x^{2} y + 5 x \frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 2 \frac{d y}{d x}^{2} + 2 y \frac{d ^{2} y}{d x ^{2}}

e x p an d \frac{6}{8}

e x p an d u (6, - 3, 6)

e x p an d \frac{x}{3} - (\frac{x}{2} - \frac{1}{3} (\frac{2 x}{3} - (\frac{1}{3} - 6 x)) = 1)

e x p an d (z - 1) (z - e^{- T})

e x p an d 2 (ln (x)) + 2 (l) + 2 (2 n - 1)