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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

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

s im pl i f y 12 (1683 - 1)

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

e x p an d 7 (x - 6)