derivative of ((3x-2)/(5x))

Lösung

\frac{d}{d x} (\frac{( 3 x - 2 )}{5 x})

\frac{2}{5 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( 3 x - 2 )}{5 x})

Entferne die Konstante:

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

= \frac{1}{5} \frac{d}{d x} (\frac{3 x - 2}{x})

Wende die Quotientenregel an:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( 3 x - 2 ) x - \frac{d x}{d x} ( 3 x - 2 )}{x ^{2}}

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

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

= \frac{1}{5} \cdot \frac{3 x - 1 \cdot ( 3 x - 2 )}{x ^{2}}

Vereinfache

\frac{1}{5} \cdot \frac{3 x - 1 \cdot ( 3 x - 2 )}{x ^{2}} : \frac{2}{5 x ^{2}}

= \frac{2}{5 x ^{2}}

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