(d^2)/(dx^2)((y)(sqrt(x)+10x^2))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (x + 10 x^{2}))

\frac{4 x \frac{d y}{d x} + 80 x ^{\frac{3}{2}} y + 160 x ^{\frac{5}{2}} \frac{d y}{d x} + 4 x x ^{\frac{3}{2}} \frac{d ^{2} y}{d x ^{2}} + 40 x ^{\frac{7}{2}} \frac{d ^{2} y}{d x ^{2}} - y}{4 x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (x + 10 x^{2}))

\frac{d}{d x} (y (x + 10 x^{2})) = \frac{d y}{d x} (x + 10 x^{2}) + (\frac{1}{2 x} + 20 x) y

= \frac{d}{d x} (\frac{d y}{d x} (x + 10 x^{2}) + (\frac{1}{2 x} + 20 x) y)

\frac{d}{d x} (\frac{d y}{d x} (x + 10 x^{2}) + (\frac{1}{2 x} + 20 x) y) = \frac{4 x \frac{d y}{d x} + 80 x ^{\frac{3}{2}} y + 160 x ^{\frac{5}{2}} \frac{d y}{d x} + 4 x x ^{\frac{3}{2}} \frac{d ^{2} y}{d x ^{2}} + 40 x ^{\frac{7}{2}} \frac{d ^{2} y}{d x ^{2}} - y}{4 x ^{\frac{3}{2}}}

= \frac{4 x \frac{d y}{d x} + 80 x ^{\frac{3}{2}} y + 160 x ^{\frac{5}{2}} \frac{d y}{d x} + 4 x x ^{\frac{3}{2}} \frac{d ^{2} y}{d x ^{2}} + 40 x ^{\frac{7}{2}} \frac{d ^{2} y}{d x ^{2}} - y}{4 x ^{\frac{3}{2}}}

s im pl i f y (\frac{x + 7}{x} + 3 x) 10

e x p an d \frac{6}{( x + 4 ) ( x - 1 )}

e x p an d A (- 13, - 15) y B (5, - 19)

e x p an d (1 - 32) (3 + 52)

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