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

Lösung

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

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

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

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

\frac{d}{d x} (- x^{2} \frac{d y}{d x} - 2 x y + 9 y^{2} \frac{d y}{d x}) = - x^{2} \frac{d ^{2} y}{d x ^{2}} - 4 x \frac{d y}{d x} - 2 y + 18 y \frac{d y}{d x}^{2} + 9 y^{2} \frac{d ^{2} y}{d x ^{2}}

= - x^{2} \frac{d ^{2} y}{d x ^{2}} - 4 x \frac{d y}{d x} - 2 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^{2} + 1) arccot (x)

e x p an d i (x + i y)^{2} + 3 x + 3 i y

e x p an d (6 x - 3 x^{2}) e^{x}

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

s im pl i f y \frac{2 ( x + 5 )}{3 3 x} + x^{\frac{2}{3}}