(d^2)/(dx^2)((y)y^2(6-2x))

Lösung

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

36 y \frac{d y}{d x}^{2} - 12 x y \frac{d y}{d x}^{2} + 18 y^{2} \frac{d ^{2} y}{d x ^{2}} - 6 x y^{2} \frac{d ^{2} y}{d x ^{2}} - 12 y^{2} \frac{d y}{d x}

Schritte zur Lösung

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

Vereinfache

(y) y^{2} (6 - 2 x) : y^{3} (6 - 2 x)

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

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

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

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

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

s im pl i f y (3 p - 5) (p + 55)

s im pl i f y (x + 4) (sin (6 x)) (cot (x^{2} + 4 x))

e x p an d (x^{2} - 2 x y + 3 y^{2}) d x + (y^{2} + 6 x y - x^{2}) d y

e x p an d \frac{2 x ^{2} - 4 x - 3}{( x + 1 ) ( 2 x - 1 )}

e x p an d \frac{2 s}{( s - 1 ) ( s ^{2} + 25 )}