derivative (1-4ln(x))/(x^5)

Lösung

ableitung von

\frac{1 - 4 ln ( x )}{x ^{5}}

- \frac{- 20 ln ( x ) + 9}{x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1 - 4 ln ( x )}{x ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 1 - 4 ln ( x ) ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( 1 - 4 ln ( x ) )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (1 - 4 ln (x)) = - \frac{4}{x}

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{( - \frac{4}{x} ) x ^{5} - 5 x ^{4} ( 1 - 4 ln ( x ) )}{( x ^{5} ) ^{2}}

Vereinfache

\frac{( - \frac{4}{x} ) x ^{5} - 5 x ^{4} ( 1 - 4 ln ( x ) )}{( x ^{5} ) ^{2}} : - \frac{- 20 ln ( x ) + 9}{x ^{6}}

= - \frac{- 20 ln ( x ) + 9}{x ^{6}}

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