erweitern (ln(x)-1)/((ln(x))^2)

Lösung

erweitern

\frac{ln ( x ) - 1}{( ln ( x ) ) ^{2}}

\frac{1}{ln ( x )} - \frac{1}{ln ^{2} ( x )}

Schritte zur Lösung

\frac{ln ( x ) - 1}{ln ^{2} ( x )}

Wende Bruchregel an:

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

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

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

Streiche

\frac{ln ( x )}{ln ^{2} ( x )} : \frac{1}{ln ( x )}

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

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

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

s im pl i f y (1 + \frac{1}{n + 1}) (1 - \frac{n}{( n + 1 ) ^{2}})

e x p an d ln (x) (x + 2)

e x p an d (1 - x) d x