(d^2)/(dx^2)((y)(12x-7+8/(x^3)))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (12 x - 7 + \frac{8}{x ^{3}}))

\frac{d ^{2} y}{d x ^{2}} (12 x - 7 + \frac{8}{x ^{3}}) + 2 (- \frac{24}{x ^{4}} + 12) \frac{d y}{d x} + \frac{96 y}{x ^{5}}

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (12 x - 7 + \frac{8}{x ^{3}}))

\frac{d}{d x} (y (12 x - 7 + \frac{8}{x ^{3}})) = \frac{d y}{d x} (12 x - 7 + \frac{8}{x ^{3}}) + (- \frac{24}{x ^{4}} + 12) y

= \frac{d}{d x} (\frac{d y}{d x} (12 x - 7 + \frac{8}{x ^{3}}) + (- \frac{24}{x ^{4}} + 12) y)

\frac{d}{d x} (\frac{d y}{d x} (12 x - 7 + \frac{8}{x ^{3}}) + (- \frac{24}{x ^{4}} + 12) y) = \frac{d ^{2} y}{d x ^{2}} (12 x - 7 + \frac{8}{x ^{3}}) + 2 (- \frac{24}{x ^{4}} + 12) \frac{d y}{d x} + \frac{96 y}{x ^{5}}

= \frac{d ^{2} y}{d x ^{2}} (12 x - 7 + \frac{8}{x ^{3}}) + 2 (- \frac{24}{x ^{4}} + 12) \frac{d y}{d x} + \frac{96 y}{x ^{5}}

s im pl i f y (x^{2} + 9 + 6)^{2}

e x p an d 6 (ln (x) + 1)

e x p an d \frac{( k + 1 ) ( 3 k + 2 )}{2}

e x p an d (5 + 7)^{4}

e x p an d \frac{k ( k + 1 ) ( 2 k + 1 )}{6}