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Beliebt Rechnen >

derivative of-(3x+1/(x^2))

Lösung

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

Lösung

- \frac{- 3 x - 2}{x ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (3 x + 1) = 3

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

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

Streiche

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

= - \frac{- 3 x - 2}{x ^{3}}

Graph

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