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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

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