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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

e x p an d \frac{1}{S ( S ^{2} + 0.2 S + 1 )}

e x p an d (x + y - 1) d x + (y - x - 5) d y

e x p an d (x (4 y d x + 2 x d y) + y^{3} (3 y x + 5 x d y)) (x^{α} y^{β})

e x p an d \frac{- 3 x ^{2} - 3 x - 10}{x ^{2} ( - 3 x ^{2} + 24 x )}

s im pl i f y 3 x (3 x^{2} - 8 3 x)