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Beliebt Rechnen >

derivative (sqrt(x))/(x^2)

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= - \frac{3}{2 x ^{\frac{5}{2}}}

Graph

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