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

Lösung

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

2 x^{3} \frac{d ^{2} y}{d x ^{2}} + 12 x^{2} \frac{d y}{d x} + 12 x y - 18 y \frac{d y}{d x}^{2} - 9 y^{2} \frac{d ^{2} y}{d x ^{2}}

Schritte zur Lösung

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

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

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

\frac{d}{d x} (2 x^{3} \frac{d y}{d x} + 6 x^{2} y - 9 y^{2} \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 - 18 y \frac{d y}{d x}^{2} - 9 y^{2} \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 - 18 y \frac{d y}{d x}^{2} - 9 y^{2} \frac{d ^{2} y}{d x ^{2}}

e x p an d (x - 4) (x - 2 + 7)

e x p an d \frac{e ^{- 0.5 x} ( x + 1 )}{x ( x + 2 ) ( x + 3 )}

e x p an d \frac{3 ( 3 3 - π )}{27 - π ^{2}}

e x p an d (x^{5} - 2 x^{2} + 1) l e f t (x^{3} - x^{2} + 1)

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