erweitern (1-1/(x^2))''(2+x)+(1-1/(x^2))(2+x)'

Lösung

erweitern

(1 - \frac{1}{x ^{2}})^{''} \cdot (2 + x) + (1 - \frac{1}{x ^{2}}) \cdot (2 + x)^{'}

2 (1 - \frac{1}{x ^{2}})'' + x (1 - \frac{1}{x ^{2}})'' + (2 + x)' - \frac{( 2 + x ) '}{x ^{2}}

Schritte zur Lösung

(1 - \frac{1}{x ^{2}})^{''} (2 + x) + (1 - \frac{1}{x ^{2}}) (2 + x)^{'}

Multipliziere aus

(1 - \frac{1}{x ^{2}})^{''} (2 + x) : 2 (1 - \frac{1}{x ^{2}})^{''} + x (1 - \frac{1}{x ^{2}})^{''}

= 2 (1 - \frac{1}{x ^{2}})^{''} + x (1 - \frac{1}{x ^{2}})^{''} + (1 - \frac{1}{x ^{2}}) (2 + x)^{'}

Multipliziere aus

(2 + x)^{'} (1 - \frac{1}{x ^{2}}) : (2 + x)^{'} - \frac{( 2 + x ) ^{'}}{x ^{2}}

= 2 (1 - \frac{1}{x ^{2}})^{''} + x (1 - \frac{1}{x ^{2}})^{''} + (2 + x)^{'} - \frac{( 2 + x ) ^{'}}{x ^{2}}

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

e x p an d \frac{4 ( k + 6 )}{k ^{2} + 10 k + 21}

e x p an d \frac{x ^{2} + 2 x + 12}{2 ( x + 2 )}

e x p an d 30 (\frac{1}{3} sin (3 x) - \frac{1}{2} cos (2 x) + \frac{1}{5} e^{5 x})

\frac{d}{d y} ((x) (- 5 x^{2} + 20 x + 2))