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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

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