derivative (8x^2+2)/(x^2)

Lösung

ableitung von

\frac{8 x ^{2} + 2}{x ^{2}}

- \frac{4}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x ^{2} + 2}{x ^{2}})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (8 x^{2} + 2) = 16 x

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

= \frac{16 x x ^{2} - 2 x ( 8 x ^{2} + 2 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{16 x x ^{2} - 2 x ( 8 x ^{2} + 2 )}{( x ^{2} ) ^{2}} : - \frac{4}{x ^{3}}

= - \frac{4}{x ^{3}}

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