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

Lösung

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

- 36 x^{3} y^{2} \frac{d y}{d x}^{2} - 12 x^{3} y^{3} \frac{d ^{2} y}{d x ^{2}} - 72 x^{2} y^{3} \frac{d y}{d x} - 6 x^{2} y \frac{d y}{d x}^{2} - 3 x^{2} y^{2} \frac{d ^{2} y}{d x ^{2}} - 12 x y^{2} \frac{d y}{d x} - 18 x y^{4} - 6 x \frac{d y}{d x}^{2} - 6 x y \frac{d ^{2} y}{d x ^{2}} - 12 y \frac{d y}{d x} - 2 y^{3} - 24 y^{2} \frac{d y}{d x}^{2} - 8 y^{3} \frac{d ^{2} y}{d x ^{2}}

Schritte zur Lösung

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

\frac{d}{d x} (y^{2} (- 3 x^{3} y^{2} - x^{2} y - 3 x - 2 y^{2})) = - 12 x^{3} y^{3} \frac{d y}{d x} - 3 x^{2} y^{2} \frac{d y}{d x} - 9 x^{2} y^{4} - 6 x y \frac{d y}{d x} - 2 x y^{3} - 8 y^{3} \frac{d y}{d x} - 3 y^{2}

= \frac{d}{d x} (- 12 x^{3} y^{3} \frac{d y}{d x} - 3 x^{2} y^{2} \frac{d y}{d x} - 9 x^{2} y^{4} - 6 x y \frac{d y}{d x} - 2 x y^{3} - 8 y^{3} \frac{d y}{d x} - 3 y^{2})

\frac{d}{d x} (- 12 x^{3} y^{3} \frac{d y}{d x} - 3 x^{2} y^{2} \frac{d y}{d x} - 9 x^{2} y^{4} - 6 x y \frac{d y}{d x} - 2 x y^{3} - 8 y^{3} \frac{d y}{d x} - 3 y^{2}) = - 36 x^{3} y^{2} \frac{d y}{d x}^{2} - 12 x^{3} y^{3} \frac{d ^{2} y}{d x ^{2}} - 72 x^{2} y^{3} \frac{d y}{d x} - 6 x^{2} y \frac{d y}{d x}^{2} - 3 x^{2} y^{2} \frac{d ^{2} y}{d x ^{2}} - 12 x y^{2} \frac{d y}{d x} - 18 x y^{4} - 6 x \frac{d y}{d x}^{2} - 6 x y \frac{d ^{2} y}{d x ^{2}} - 12 y \frac{d y}{d x} - 2 y^{3} - 24 y^{2} \frac{d y}{d x}^{2} - 8 y^{3} \frac{d ^{2} y}{d x ^{2}}

= - 36 x^{3} y^{2} \frac{d y}{d x}^{2} - 12 x^{3} y^{3} \frac{d ^{2} y}{d x ^{2}} - 72 x^{2} y^{3} \frac{d y}{d x} - 6 x^{2} y \frac{d y}{d x}^{2} - 3 x^{2} y^{2} \frac{d ^{2} y}{d x ^{2}} - 12 x y^{2} \frac{d y}{d x} - 18 x y^{4} - 6 x \frac{d y}{d x}^{2} - 6 x y \frac{d ^{2} y}{d x ^{2}} - 12 y \frac{d y}{d x} - 2 y^{3} - 24 y^{2} \frac{d y}{d x}^{2} - 8 y^{3} \frac{d ^{2} y}{d x ^{2}}

e x p an d cos (t - 1) U (t - 1)

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

e x p an d \frac{( e ^{- 7 s} )}{( s - 3 ) ( s - 1 )}

e x p an d 2 x y d x + (1 + x^{2}) d y

\frac{d}{d t} ((x) (t + 1))