derivative of (2x-1/x)

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

\int - csc (x) cot (x) d x

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