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Beliebt Rechnen >

derivative y=(2x^2-x+4)/x

Lösung

ableitung von

y = \frac{2 x ^{2} - x + 4}{x}

Lösung

\frac{2 x ^{2} - 4}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{2 x ^{2} - 4}{x ^{2}}

Graph

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