derivative of (-2ln(x+1)/(x^3))

Lösung

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

- \frac{- 6 ln ( x ) + 5}{x ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( - \frac{2}{x} ) x ^{3} - 3 x ^{2} ( - 2 ln ( x ) + 1 )}{( x ^{3} ) ^{2}} : - \frac{- 6 ln ( x ) + 5}{x ^{4}}

= - \frac{- 6 ln ( x ) + 5}{x ^{4}}

l a pl a ce t r an s f or m 3 x

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