(d^2)/(dx^2)((y)(x^4+y^2))

Lösung

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

x^{4} \frac{d ^{2} y}{d x ^{2}} + 8 x^{3} \frac{d y}{d x} + 12 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^{4} + y^{2}))

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

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

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

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

e x p an d (x - 5) \cdot (x - 1 + 2)

e x p an d \frac{( x ^{2} + 29 ) - 2 x}{( x ^{2} + 29 ) ^{2}}

e x p an d \frac{2}{cos ( x ) ( 1 - sin ( x ) )}

s im pl i f y cos (x) (- \frac{1}{2} (x - sin (x) cos (x)))