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Beliebt Rechnen >

derivative (4x^5+7)/(x^3)

Lösung

ableitung von

\frac{4 x ^{5} + 7}{x ^{3}}

Lösung

\frac{8 x ^{5} - 21}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{5} + 7}{x ^{3}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x ^{5} + 7 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 4 x ^{5} + 7 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (4 x^{5} + 7) = 20 x^{4}

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

= \frac{20 x ^{4} x ^{3} - 3 x ^{2} ( 4 x ^{5} + 7 )}{( x ^{3} ) ^{2}}

Vereinfache

\frac{20 x ^{4} x ^{3} - 3 x ^{2} ( 4 x ^{5} + 7 )}{( x ^{3} ) ^{2}} : \frac{8 x ^{5} - 21}{x ^{4}}

= \frac{8 x ^{5} - 21}{x ^{4}}

Graph

Beliebte Beispiele

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