derivative (x^8-2x^4-10x)/(x^4)

Lösung

ableitung von

\frac{x ^{8} - 2 x ^{4} - 10 x}{x ^{4}}

\frac{2 ( 2 x ^{7} + 15 )}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{8} - 2 x ^{4} - 10 x}{x ^{4}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{8} - 2 x ^{4} - 10 x ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( x ^{8} - 2 x ^{4} - 10 x )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (x^{8} - 2 x^{4} - 10 x) = 8 x^{7} - 8 x^{3} - 10

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{( 8 x ^{7} - 8 x ^{3} - 10 ) x ^{4} - 4 x ^{3} ( x ^{8} - 2 x ^{4} - 10 x )}{( x ^{4} ) ^{2}}

Vereinfache

\frac{( 8 x ^{7} - 8 x ^{3} - 10 ) x ^{4} - 4 x ^{3} ( x ^{8} - 2 x ^{4} - 10 x )}{( x ^{4} ) ^{2}} : \frac{2 ( 2 x ^{7} + 15 )}{x ^{4}}

= \frac{2 ( 2 x ^{7} + 15 )}{x ^{4}}

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