(d^3)/(dx^3)((y)(5x-8)^3)

Lösung

\frac{d ^{3}}{d x ^{3}} ((y) (5 x - 8)^{3})

2250 x \frac{d y}{d x} + (5 x - 8)^{3} \frac{d ^{3} y}{d x ^{3}} + 45 (5 x - 8)^{2} \frac{d ^{2} y}{d x ^{2}} - 3600 \frac{d y}{d x} + 750 y

Schritte zur Lösung

\frac{d ^{3}}{d x ^{3}} ((y) (5 x - 8)^{3})

\frac{d}{d x} (y (5 x - 8)^{3}) = \frac{d y}{d x} (5 x - 8)^{3} + 15 (5 x - 8)^{2} y

= \frac{d ^{2}}{d x ^{2}} (\frac{d y}{d x} (5 x - 8)^{3} + 15 (5 x - 8)^{2} y)

\frac{d}{d x} (\frac{d y}{d x} (5 x - 8)^{3} + 15 (5 x - 8)^{2} y) = \frac{d ^{2} y}{d x ^{2}} (5 x - 8)^{3} + 30 \frac{d y}{d x} (5 x - 8)^{2} + 750 x y - 1200 y

= \frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (5 x - 8)^{3} + 30 \frac{d y}{d x} (5 x - 8)^{2} + 750 x y - 1200 y)

\frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (5 x - 8)^{3} + 30 \frac{d y}{d x} (5 x - 8)^{2} + 750 x y - 1200 y) = 2250 x \frac{d y}{d x} + (5 x - 8)^{3} \frac{d ^{3} y}{d x ^{3}} + 45 (5 x - 8)^{2} \frac{d ^{2} y}{d x ^{2}} - 3600 \frac{d y}{d x} + 750 y

= 2250 x \frac{d y}{d x} + (5 x - 8)^{3} \frac{d ^{3} y}{d x ^{3}} + 45 (5 x - 8)^{2} \frac{d ^{2} y}{d x ^{2}} - 3600 \frac{d y}{d x} + 750 y

e x p an d (A x + B) e^{2 x}

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