erweitern (2019+ln(x-1)(x-1))/(e^x)

Lösung

erweitern

\frac{2019 + ln ( x - 1 ) ( x - 1 )}{e ^{x}}

\frac{2019}{e ^{x}} + \frac{x ln ( x - 1 )}{e ^{x}} - \frac{ln ( x - 1 )}{e ^{x}}

Schritte zur Lösung

\frac{2019 + ln ( x - 1 ) ( x - 1 )}{e ^{x}}

Multipliziere aus

2019 + ln (x - 1) (x - 1) : 2019 + x ln (x - 1) - ln (x - 1)

= \frac{2019 + x ln ( x - 1 ) - ln ( x - 1 )}{e ^{x}}

Wende Bruchregel an:

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

\frac{2019 + x ln ( x - 1 ) - ln ( x - 1 )}{e ^{x}} = \frac{2019}{e ^{x}} + \frac{x ln ( x - 1 )}{e ^{x}} - \frac{ln ( x - 1 )}{e ^{x}}

= \frac{2019}{e ^{x}} + \frac{x ln ( x - 1 )}{e ^{x}} - \frac{ln ( x - 1 )}{e ^{x}}

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

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

s im pl i f y (3 n - 3) 2

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

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