derivative of x/((1-x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

n = 1 \sum \infty ln (1 + \frac{2}{n})

d er i v a t i v e y = \frac{2 x}{5 - cot ( x )}

\frac{\partial}{\partial y} (4 x^{2} + 3 y^{4})

\int cot^{2} (3 x) d x

\int (1 + x)^{3} d x