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Beliebt Rechnen >

derivative (2xsqrt(3x-1))/(5x)

Lösung

ableitung von

\frac{2 x 3 x - 1}{5 x}

Lösung

\frac{3}{5 3 x - 1}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x 3 x - 1) = \frac{9 x - 2}{2 3 x - 1}

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

= \frac{2}{5} \cdot \frac{\frac{9 x - 2}{2 3 x - 1} x - 1 \cdot x 3 x - 1}{x ^{2}}

Vereinfache

\frac{2}{5} \cdot \frac{\frac{9 x - 2}{2 3 x - 1} x - 1 \cdot x 3 x - 1}{x ^{2}} : \frac{3}{5 3 x - 1}

= \frac{3}{5 3 x - 1}

Graph

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