(d^3)/(dx^3)((y)(2x-1)^4)

解答

\frac{d ^{3}}{d x ^{3}} ((y) (2 x - 1)^{4})

\frac{d ^{3} y}{d x ^{3}} (2 x - 1)^{4} + 24 \frac{d ^{2} y}{d x ^{2}} (2 x - 1)^{3} + 144 \frac{d y}{d x} (2 x - 1)^{2} + 384 x y - 192 y

求解步骤

\frac{d ^{3}}{d x ^{3}} ((y) (2 x - 1)^{4})

\frac{d}{d x} (y (2 x - 1)^{4}) = \frac{d y}{d x} (2 x - 1)^{4} + 8 (2 x - 1)^{3} y

= \frac{d ^{2}}{d x ^{2}} (\frac{d y}{d x} (2 x - 1)^{4} + 8 (2 x - 1)^{3} y)

\frac{d}{d x} (\frac{d y}{d x} (2 x - 1)^{4} + 8 (2 x - 1)^{3} y) = \frac{d ^{2} y}{d x ^{2}} (2 x - 1)^{4} + 16 \frac{d y}{d x} (2 x - 1)^{3} + 48 (2 x - 1)^{2} y

= \frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (2 x - 1)^{4} + 16 \frac{d y}{d x} (2 x - 1)^{3} + 48 (2 x - 1)^{2} y)

\frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (2 x - 1)^{4} + 16 \frac{d y}{d x} (2 x - 1)^{3} + 48 (2 x - 1)^{2} y) = \frac{d ^{3} y}{d x ^{3}} (2 x - 1)^{4} + 24 \frac{d ^{2} y}{d x ^{2}} (2 x - 1)^{3} + 144 \frac{d y}{d x} (2 x - 1)^{2} + 384 x y - 192 y

= \frac{d ^{3} y}{d x ^{3}} (2 x - 1)^{4} + 24 \frac{d ^{2} y}{d x ^{2}} (2 x - 1)^{3} + 144 \frac{d y}{d x} (2 x - 1)^{2} + 384 x y - 192 y

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