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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int_{0}^{2.5} 25 - x^{2} d x

\int \frac{1}{x ^{2} + 14} d x

s im pl i f y sin (x + y)

\int sin (b t) d t

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