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Beliebt Rechnen >

derivative of (sqrt(2x-3)/(x^2))

Lösung

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

Lösung

\frac{3 ( - x + 2 )}{x ^{3} 2 x - 3}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Vereinfache

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

= \frac{3 ( - x + 2 )}{x ^{3} 2 x - 3}

Graph

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