(d^3)/(dx^3)((y)(3x^3+6x^2-4x))

Lösung

\frac{d ^{3}}{d x ^{3}} ((y) (3 x^{3} + 6 x^{2} - 4 x))

3 x^{3} \frac{d ^{3} y}{d x ^{3}} + 6 x^{2} \frac{d ^{3} y}{d x ^{3}} + 27 x^{2} \frac{d ^{2} y}{d x ^{2}} - 4 x \frac{d ^{3} y}{d x ^{3}} + 36 x \frac{d ^{2} y}{d x ^{2}} + 54 x \frac{d y}{d x} - 12 \frac{d ^{2} y}{d x ^{2}} + 36 \frac{d y}{d x} + 18 y

Schritte zur Lösung

\frac{d ^{3}}{d x ^{3}} ((y) (3 x^{3} + 6 x^{2} - 4 x))

\frac{d}{d x} (y (3 x^{3} + 6 x^{2} - 4 x)) = \frac{d y}{d x} (3 x^{3} + 6 x^{2} - 4 x) + (9 x^{2} + 12 x - 4) y

= \frac{d ^{2}}{d x ^{2}} (\frac{d y}{d x} (3 x^{3} + 6 x^{2} - 4 x) + (9 x^{2} + 12 x - 4) y)

\frac{d}{d x} (\frac{d y}{d x} (3 x^{3} + 6 x^{2} - 4 x) + (9 x^{2} + 12 x - 4) y) = \frac{d ^{2} y}{d x ^{2}} (3 x^{3} + 6 x^{2} - 4 x) + 2 \frac{d y}{d x} (9 x^{2} + 12 x - 4) + (18 x + 12) y

= \frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (3 x^{3} + 6 x^{2} - 4 x) + 2 \frac{d y}{d x} (9 x^{2} + 12 x - 4) + (18 x + 12) y)

\frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (3 x^{3} + 6 x^{2} - 4 x) + 2 \frac{d y}{d x} (9 x^{2} + 12 x - 4) + (18 x + 12) y) = 3 x^{3} \frac{d ^{3} y}{d x ^{3}} + 6 x^{2} \frac{d ^{3} y}{d x ^{3}} + 27 x^{2} \frac{d ^{2} y}{d x ^{2}} - 4 x \frac{d ^{3} y}{d x ^{3}} + 36 x \frac{d ^{2} y}{d x ^{2}} + 54 x \frac{d y}{d x} - 12 \frac{d ^{2} y}{d x ^{2}} + 36 \frac{d y}{d x} + 18 y

= 3 x^{3} \frac{d ^{3} y}{d x ^{3}} + 6 x^{2} \frac{d ^{3} y}{d x ^{3}} + 27 x^{2} \frac{d ^{2} y}{d x ^{2}} - 4 x \frac{d ^{3} y}{d x ^{3}} + 36 x \frac{d ^{2} y}{d x ^{2}} + 54 x \frac{d y}{d x} - 12 \frac{d ^{2} y}{d x ^{2}} + 36 \frac{d y}{d x} + 18 y

e x p an d 7350 (z - e^{- T}) (z - e^{- 2 T}) (z - e^{- 7 T})

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

e x p an d sin (2 t) U (t - π)

\frac{\partial}{\partial x} ((y) (z + x^{2} + y^{2}))

e x p an d A (- 4, - \frac{3}{2}) y B (5, - 2)