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Beliebt Rechnen >

derivative f(x)=(3x^2-x+1)/x

Lösung

ableitung von

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

Lösung

\frac{3 x ^{2} - 1}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (3 x^{2} - x + 1) = 6 x - 1

\frac{d x}{d x} = 1

= \frac{( 6 x - 1 ) x - 1 \cdot ( 3 x ^{2} - x + 1 )}{x ^{2}}

Vereinfache

\frac{( 6 x - 1 ) x - 1 \cdot ( 3 x ^{2} - x + 1 )}{x ^{2}} : \frac{3 x ^{2} - 1}{x ^{2}}

= \frac{3 x ^{2} - 1}{x ^{2}}

Graph

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