derivative f(x)=(1300+8x-0.0004x^2)/x

Lösung

ableitung von

f (x) = \frac{1300 + 8 x - 0.0004 x ^{2}}{x}

\frac{- 0.0004 x ^{2} - 1300}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1300 + 8 x - 0.0004 x ^{2}}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 1300 + 8 x - 0.0004 x ^{2} ) x - \frac{d x}{d x} ( 1300 + 8 x - 0.0004 x ^{2} )}{x ^{2}}

\frac{d}{d x} (1300 + 8 x - 0.0004 x^{2}) = - 0.0008 x + 8

\frac{d x}{d x} = 1

= \frac{( - 0.0008 x + 8 ) x - 1 \cdot ( 1300 + 8 x - 0.0004 x ^{2} )}{x ^{2}}

Vereinfache

\frac{( - 0.0008 x + 8 ) x - 1 \cdot ( 1300 + 8 x - 0.0004 x ^{2} )}{x ^{2}} : \frac{- 0.0004 x ^{2} - 1300}{x ^{2}}

= \frac{- 0.0004 x ^{2} - 1300}{x ^{2}}

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