derivative f(x)=\sqrt[6]{x^5}

Lösung

ableitung von

f (x) = 6 x^{5}

\frac{5 x ^{4}}{6 ( x ^{5} ) ^{\frac{5}{6}}}

Schritte zur Lösung

\frac{d}{d x} (6 x^{5})

Wende die Kettenregel an:

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

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

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

= \frac{1}{6 ( x ^{5} ) ^{\frac{5}{6}}} \cdot 5 x^{4}

Vereinfache

\frac{1}{6 ( x ^{5} ) ^{\frac{5}{6}}} \cdot 5 x^{4} : \frac{5 x ^{4}}{6 ( x ^{5} ) ^{\frac{5}{6}}}

= \frac{5 x ^{4}}{6 ( x ^{5} ) ^{\frac{5}{6}}}

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