derivative f(x)=16x^{1/8}

Lösung

ableitung von

f (x) = 16 x^{\frac{1}{8}}

\frac{2}{x ^{\frac{7}{8}}}

Schritte zur Lösung

\frac{d}{d x} (16 x^{\frac{1}{8}})

Entferne die Konstante:

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

= 16 \frac{d}{d x} (x^{\frac{1}{8}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 16 \cdot \frac{1}{8} x^{\frac{1}{8} - 1}

Vereinfache

16 \cdot \frac{1}{8} x^{\frac{1}{8} - 1} : \frac{2}{x ^{\frac{7}{8}}}

= \frac{2}{x ^{\frac{7}{8}}}

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