erweitern-(2(x-1)^3sinh(x))/(cosh^3(x))

Lösung

erweitern

- \frac{2 ( x - 1 ) ^{3} sinh ( x )}{cosh ^{3} ( x )}

- \frac{2 x ^{3} sinh ( x )}{cosh ^{3} ( x )} + \frac{6 x ^{2} sinh ( x )}{cosh ^{3} ( x )} - \frac{6 x sinh ( x )}{cosh ^{3} ( x )} + \frac{2 sinh ( x )}{cosh ^{3} ( x )}

Schritte zur Lösung

- \frac{2 ( x - 1 ) ^{3} sinh ( x )}{cosh ^{3} ( x )}

(x - 1)^{3} = x^{3} - 3 x^{2} + 3 x - 1

= - \frac{2 sinh ( x ) ( x ^{3} - 3 x ^{2} + 3 x - 1 )}{cosh ^{3} ( x )}

Multipliziere aus

2 (x^{3} - 3 x^{2} + 3 x - 1) sinh (x) : 2 x^{3} sinh (x) - 6 x^{2} sinh (x) + 6 x sinh (x) - 2 sinh (x)

= - \frac{2 x ^{3} sinh ( x ) - 6 x ^{2} sinh ( x ) + 6 x sinh ( x ) - 2 sinh ( x )}{cosh ^{3} ( x )}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 x ^{3} sinh ( x ) - 6 x ^{2} sinh ( x ) + 6 x sinh ( x ) - 2 sinh ( x )}{cosh ^{3} ( x )} = - (\frac{2 x ^{3} sinh ( x )}{cosh ^{3} ( x )}) - (- \frac{6 x ^{2} sinh ( x )}{cosh ^{3} ( x )}) - (\frac{6 x sinh ( x )}{cosh ^{3} ( x )}) - (- \frac{2 sinh ( x )}{cosh ^{3} ( x )})

= - (\frac{2 x ^{3} sinh ( x )}{cosh ^{3} ( x )}) - (- \frac{6 x ^{2} sinh ( x )}{cosh ^{3} ( x )}) - (\frac{6 x sinh ( x )}{cosh ^{3} ( x )}) - (- \frac{2 sinh ( x )}{cosh ^{3} ( x )})

Entferne die Klammern:

(a) = a, - (- a) = a

= - \frac{2 x ^{3} sinh ( x )}{cosh ^{3} ( x )} + \frac{6 x ^{2} sinh ( x )}{cosh ^{3} ( x )} - \frac{6 x sinh ( x )}{cosh ^{3} ( x )} + \frac{2 sinh ( x )}{cosh ^{3} ( x )}

e x p an d sin ((1 - n) π)

e x p an d \frac{32 x ^{3} - 204 x ^{2}}{( 4 x - 17 ) ^{2}}

e x p an d \frac{y ( - y ^{4} + 16 y ^{2} + 8 y - 32 )}{8}

s im pl i f y (x^{2} - 9 x \circ x - 9) (- 2)

s im pl i f y (b - a) (b + a)