derivative ((x^6+1))/(x^5)

Lösung

ableitung von

\frac{( x ^{6} + 1 )}{x ^{5}}

\frac{x ^{6} - 5}{x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{6} + 1}{x ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{6} + 1 ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( x ^{6} + 1 )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (x^{6} + 1) = 6 x^{5}

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

= \frac{6 x ^{5} x ^{5} - 5 x ^{4} ( x ^{6} + 1 )}{( x ^{5} ) ^{2}}

Vereinfache

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

= \frac{x ^{6} - 5}{x ^{6}}

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