(d^2)/(dx^2)((y)(y^3+7y-x^3))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (y^{3} + 7 y - x^{3}))

- x^{3} \frac{d ^{2} y}{d x ^{2}} - 6 x^{2} \frac{d y}{d x} - 6 x y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x}^{2} + 14 y \frac{d ^{2} y}{d x ^{2}}

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (y^{3} + 7 y - x^{3}))

\frac{d}{d x} (y (y^{3} + 7 y - x^{3})) = - x^{3} \frac{d y}{d x} - 3 x^{2} y + 4 y^{3} \frac{d y}{d x} + 14 y \frac{d y}{d x}

= \frac{d}{d x} (- x^{3} \frac{d y}{d x} - 3 x^{2} y + 4 y^{3} \frac{d y}{d x} + 14 y \frac{d y}{d x})

\frac{d}{d x} (- x^{3} \frac{d y}{d x} - 3 x^{2} y + 4 y^{3} \frac{d y}{d x} + 14 y \frac{d y}{d x}) = - x^{3} \frac{d ^{2} y}{d x ^{2}} - 6 x^{2} \frac{d y}{d x} - 6 x y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x}^{2} + 14 y \frac{d ^{2} y}{d x ^{2}}

= - x^{3} \frac{d ^{2} y}{d x ^{2}} - 6 x^{2} \frac{d y}{d x} - 6 x y + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x}^{2} + 14 y \frac{d ^{2} y}{d x ^{2}}

e x p an d - \frac{1}{s ( 3 s - 3 )}

e x p an d \frac{( s )}{( s - 2 ) ( s - 3 ) ( s - 6 )}

e x p an d x - 1^{2}

e x p an d \frac{5 ( 5 + 7 )}{3}

s im pl i f y 10 (10 + y 30)