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

Lösung

ableitung von

\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}}

\frac{\partial}{\partial x} (7 x e^{x y})

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