(d^2)/(dx^2)((y)(2x^{5/3}-5x^{4/3}))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}))

\frac{- 120 x \frac{d y}{d x} + 60 x ^{\frac{4}{3}} \frac{d y}{d x} + 20 x ^{\frac{1}{3}} y - 20 y + 18 x ^{\frac{7}{3}} \frac{d ^{2} y}{d x ^{2}} - 45 x ^{2} \frac{d ^{2} y}{d x ^{2}}}{9 x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}))

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

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

\frac{d}{d x} \frac{d y}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}) + \frac{( 10 x ^{\frac{2}{3}} - 20 x ^{\frac{1}{3}} ) y}{3} = \frac{- 120 x \frac{d y}{d x} + 60 x ^{\frac{4}{3}} \frac{d y}{d x} + 20 x ^{\frac{1}{3}} y - 20 y + 18 x ^{\frac{7}{3}} \frac{d ^{2} y}{d x ^{2}} - 45 x ^{2} \frac{d ^{2} y}{d x ^{2}}}{9 x ^{\frac{2}{3}}}

= \frac{- 120 x \frac{d y}{d x} + 60 x ^{\frac{4}{3}} \frac{d y}{d x} + 20 x ^{\frac{1}{3}} y - 20 y + 18 x ^{\frac{7}{3}} \frac{d ^{2} y}{d x ^{2}} - 45 x ^{2} \frac{d ^{2} y}{d x ^{2}}}{9 x ^{\frac{2}{3}}}

e x p an d (2 x y) d x + (3 x^{2} - y x) d y

e x p an d \frac{d}{d x} (3 x^{4}) + (2 x - 1)^{2}

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

e x p an d \frac{2}{( s - 6 ) ( s + 6 )}

e x p an d lo g_{10} (\frac{57}{74})