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

Lösung

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

\frac{d ^{2} y}{d x ^{2}} (x^{2} + 2 x) (3 x - 2)^{2} + 2 (36 x^{3} + 18 x^{2} - 40 x + 8) \frac{d y}{d x} + (108 x^{2} + 36 x - 40) y

Schritte zur Lösung

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

\frac{d}{d x} (y (x^{2} + 2 x) (3 x - 2)^{2}) = \frac{d y}{d x} (x^{2} + 2 x) (3 x - 2)^{2} + (36 x^{3} + 18 x^{2} - 40 x + 8) y

= \frac{d}{d x} (\frac{d y}{d x} (x^{2} + 2 x) (3 x - 2)^{2} + (36 x^{3} + 18 x^{2} - 40 x + 8) y)

\frac{d}{d x} (\frac{d y}{d x} (x^{2} + 2 x) (3 x - 2)^{2} + (36 x^{3} + 18 x^{2} - 40 x + 8) y) = \frac{d ^{2} y}{d x ^{2}} (x^{2} + 2 x) (3 x - 2)^{2} + 2 (36 x^{3} + 18 x^{2} - 40 x + 8) \frac{d y}{d x} + (108 x^{2} + 36 x - 40) y

= \frac{d ^{2} y}{d x ^{2}} (x^{2} + 2 x) (3 x - 2)^{2} + 2 (36 x^{3} + 18 x^{2} - 40 x + 8) \frac{d y}{d x} + (108 x^{2} + 36 x - 40) y

e x p an d (4, 2, - 3, 5, - 1) l e f t (2, 6, - 1, - 4, 8)

s im pl i f y (2 x - 5)^{2}

e x p an d (- 1, - 5) y

e x p an d \frac{2 - 4 e ^{- π s}}{( s ^{2} - 6 ) ( s ^{2} + 1 )} + \frac{s}{s ^{2} - 6}

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