derivative f(x)=(12-8x)/(5x^{2/5)}

Lösung

ableitung von

f (x) = \frac{12 - 8 x}{5 x ^{\frac{2}{5}}}

\frac{- 24 x - 24}{25 x ^{\frac{7}{5}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{12 - 8 x}{5 x ^{\frac{2}{5}}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{5} \frac{d}{d x} (\frac{12 - 8 x}{x ^{\frac{2}{5}}})

Wende die Quotientenregel an:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( 12 - 8 x ) x ^{\frac{2}{5}} - \frac{d}{d x} ( x ^{\frac{2}{5}} ) ( 12 - 8 x )}{( x ^{\frac{2}{5}} ) ^{2}}

\frac{d}{d x} (12 - 8 x) = - 8

\frac{d}{d x} (x^{\frac{2}{5}}) = \frac{2}{5 x ^{\frac{3}{5}}}

= \frac{1}{5} \cdot \frac{( - 8 ) x ^{\frac{2}{5}} - \frac{2}{5 x ^{\frac{3}{5}}} ( 12 - 8 x )}{( x ^{\frac{2}{5}} ) ^{2}}

Vereinfache

\frac{1}{5} \cdot \frac{( - 8 ) x ^{\frac{2}{5}} - \frac{2}{5 x ^{\frac{3}{5}}} ( 12 - 8 x )}{( x ^{\frac{2}{5}} ) ^{2}} : \frac{- 24 x - 24}{25 x ^{\frac{7}{5}}}

= \frac{- 24 x - 24}{25 x ^{\frac{7}{5}}}

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