derivative of (3x+2/(x-1))

Lösung

\frac{d}{d x} (\frac{3 x + 2}{x - 1})

- \frac{5}{( x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 2}{x - 1})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (3 x + 2) = 3

\frac{d}{d x} (x - 1) = 1

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

Vereinfache

\frac{3 ( x - 1 ) - 1 \cdot ( 3 x + 2 )}{( x - 1 ) ^{2}} : - \frac{5}{( x - 1 ) ^{2}}

= - \frac{5}{( x - 1 ) ^{2}}

\frac{d}{d x} (\frac{e ^{x}}{x + 1})

\int \frac{e ^{\frac{x}{2}}}{2} d x

n = 0 \sum \infty (- \frac{5}{8})^{n}

d er i v a t i v e lo g_{e} (\frac{1}{csc ( x )})

t a y l or (1 + x)^{\frac{1}{x}}