derivative of 5/12 x^{6/5}-5/8 x^{4/5}

Lösung

\frac{d}{d x} (\frac{5}{12} x^{\frac{6}{5}} - \frac{5}{8} x^{\frac{4}{5}})

\frac{x ^{\frac{1}{5}}}{2} - \frac{1}{2 x ^{\frac{1}{5}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{12} x^{\frac{6}{5}} - \frac{5}{8} x^{\frac{4}{5}})

Vereinfache

\frac{5}{12} x^{\frac{6}{5}} - \frac{5}{8} x^{\frac{4}{5}} : \frac{5 x ^{\frac{6}{5}}}{12} - \frac{5 x ^{\frac{4}{5}}}{8}

= \frac{d}{d x} (\frac{5 x ^{\frac{6}{5}}}{12} - \frac{5 x ^{\frac{4}{5}}}{8})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{5 x ^{\frac{6}{5}}}{12}) - \frac{d}{d x} (\frac{5 x ^{\frac{4}{5}}}{8})

\frac{d}{d x} (\frac{5 x ^{\frac{6}{5}}}{12}) = \frac{x ^{\frac{1}{5}}}{2}

\frac{d}{d x} (\frac{5 x ^{\frac{4}{5}}}{8}) = \frac{1}{2 x ^{\frac{1}{5}}}

= \frac{x ^{\frac{1}{5}}}{2} - \frac{1}{2 x ^{\frac{1}{5}}}

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