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

Lösung

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

2 x^{3} \frac{d ^{2} y}{d x ^{2}} + 12 x^{2} \frac{d y}{d x} + 12 x y + 6 y \frac{d y}{d x}^{2} + 3 y^{2} \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x}^{2} + 2 y \frac{d ^{2} y}{d x ^{2}}

Schritte zur Lösung

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

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

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

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

= 2 x^{3} \frac{d ^{2} y}{d x ^{2}} + 12 x^{2} \frac{d y}{d x} + 12 x y + 6 y \frac{d y}{d x}^{2} + 3 y^{2} \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x}^{2} + 2 y \frac{d ^{2} y}{d x ^{2}}

e x p an d tan (\frac{π}{4} + \frac{π}{6}) + cot (\frac{3 π}{4} + \frac{π}{6})

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

e x p an d (2 x + 1) (x + 1)

e x p an d (6 t - 8 sin (2 t)) (6 - 16 cos (2 t))

e x p an d - \frac{4 s ^{2} + 8 s + 2}{( s + 1 ) ^{3}}