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

Lösung

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

- \frac{4}{( 1 + 2 x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( - 2 ) ( 1 + 2 x ) - 2 ( 1 - 2 x )}{( 1 + 2 x ) ^{2}} : - \frac{4}{( 1 + 2 x ) ^{2}}

= - \frac{4}{( 1 + 2 x ) ^{2}}

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