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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{2 arctan ( x )}{1 + x ^{2}} d x

d er i v a t i v e f (x) = (x^{2} + 1)^{3} - (x^{3} + 1)^{2}

\frac{d}{d x} (- cos^{2} (2 x))

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

\frac{d}{d x} (- 32 cos (2 x))