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Beliebt Rechnen >

derivative of (log_{e}(x)/(x^2))

Lösung

\frac{d}{d x} (\frac{lo g _{e} ( x )}{x ^{2}})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{lo g _{e} ( x )}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( lo g _{e} ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) lo g _{e} ( x )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (lo g_{e} (x)) = \frac{1}{x}

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

= \frac{\frac{1}{x} x ^{2} - 2 x lo g _{e} ( x )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{\frac{1}{x} x ^{2} - 2 x lo g _{e} ( x )}{( x ^{2} ) ^{2}} : \frac{1 - 2 ln ( x )}{x ^{3}}

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

Graph

Beliebte Beispiele

y^{''}-2y^'-3y=0

y^{^{''}} - 2 y^{^{'}} - 3 y = 0

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