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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

s im pl i f y - 32 (1 - 37) + \frac{- 16 - 272 37}{27}

e x p an d (n + 2 i - n + i) n

e x p an d a (1 - e^{- b x})

e x p an d (x^{2} + 2 x - 5)^{7}

e x p an d (1 + \frac{s}{100000}) (1 + \frac{s}{98814})