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

Lösung

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

x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} - 8 x \frac{d y}{d x}^{2} - 8 x y \frac{d ^{2} y}{d x ^{2}} - 16 y \frac{d y}{d x} + 2 y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x}^{2} + 8 y \frac{d ^{2} y}{d x ^{2}}

Schritte zur Lösung

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

\frac{d}{d x} (y (x^{2} - 4 x y + y^{3} + 4 y)) = x^{2} \frac{d y}{d x} - 8 x y \frac{d y}{d x} + 2 x y + 4 y^{3} \frac{d y}{d x} + 8 y \frac{d y}{d x} - 4 y^{2}

= \frac{d}{d x} (x^{2} \frac{d y}{d x} - 8 x y \frac{d y}{d x} + 2 x y + 4 y^{3} \frac{d y}{d x} + 8 y \frac{d y}{d x} - 4 y^{2})

\frac{d}{d x} (x^{2} \frac{d y}{d x} - 8 x y \frac{d y}{d x} + 2 x y + 4 y^{3} \frac{d y}{d x} + 8 y \frac{d y}{d x} - 4 y^{2}) = x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} - 8 x \frac{d y}{d x}^{2} - 8 x y \frac{d ^{2} y}{d x ^{2}} - 16 y \frac{d y}{d x} + 2 y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x}^{2} + 8 y \frac{d ^{2} y}{d x ^{2}}

= x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} - 8 x \frac{d y}{d x}^{2} - 8 x y \frac{d ^{2} y}{d x ^{2}} - 16 y \frac{d y}{d x} + 2 y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x}^{2} + 8 y \frac{d ^{2} y}{d x ^{2}}

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)

e x p an d \frac{( x ^{2} + 6 x + 6 )}{2 ( x ^{2} + 2 x + 2 )}

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