erweitern (ln(-x+1)(-x+1)-xln(x))/(xln(x))

Lösung

erweitern

\frac{ln ( - x + 1 ) ( - x + 1 ) - x ln ( x )}{x ln ( x )}

- \frac{ln ( - x + 1 )}{ln ( x )} + \frac{ln ( - x + 1 )}{x ln ( x )} - 1

Schritte zur Lösung

\frac{ln ( - x + 1 ) ( - x + 1 ) - x ln ( x )}{x ln ( x )}

Multipliziere aus

ln (- x + 1) (- x + 1) - x ln (x) : - x ln (- x + 1) + ln (- x + 1) - x ln (x)

= \frac{- x ln ( - x + 1 ) + ln ( - x + 1 ) - x ln ( x )}{x ln ( x )}

Wende Bruchregel an:

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

\frac{- x ln ( - x + 1 ) + ln ( - x + 1 ) - x ln ( x )}{x ln ( x )} = - \frac{x ln ( - x + 1 )}{x ln ( x )} + \frac{ln ( - x + 1 )}{x ln ( x )} - \frac{x ln ( x )}{x ln ( x )}

= - \frac{x ln ( - x + 1 )}{x ln ( x )} + \frac{ln ( - x + 1 )}{x ln ( x )} - \frac{x ln ( x )}{x ln ( x )}

Wende Regel an

\frac{a}{a} = 1

\frac{x ln ( x )}{x ln ( x )} = 1

= - \frac{x ln ( - x + 1 )}{x ln ( x )} + \frac{ln ( - x + 1 )}{x ln ( x )} - 1

Streiche

\frac{x ln ( - x + 1 )}{x ln ( x )} : \frac{ln ( - x + 1 )}{ln ( x )}

= - \frac{ln ( - x + 1 )}{ln ( x )} + \frac{ln ( - x + 1 )}{x ln ( x )} - 1

e x p an d \frac{6 cos ^{3} ( s - 2 ) - 6 s ^{4} + 24 s - 48}{s ^{4} ( s - 2 )}

\frac{d}{d y} ((x) (7 x + 2 4 x))

e x p an d \frac{2 ( k ^{3} + 3 k ^{2} + 5 k + 2 )}{3}

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

e x p an d \frac{3 e ^{83}}{16} (x - 64)