derivative of 3/4 (x^2-1^{2/3})

Lösung

\frac{d}{d x} (\frac{3}{4} (x^{2} - 1)^{\frac{2}{3}})

\frac{x}{( x ^{2} - 1 ) ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{4} (x^{2} - 1)^{\frac{2}{3}})

Entferne die Konstante:

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

= \frac{3}{4} \frac{d}{d x} ((x^{2} - 1)^{\frac{2}{3}})

Wende die Kettenregel an:

\frac{2}{3 ( x ^{2} - 1 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} - 1)

= \frac{2}{3 ( x ^{2} - 1 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} - 1)

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

= \frac{3}{4} \cdot \frac{2}{3 ( x ^{2} - 1 ) ^{\frac{1}{3}}} \cdot 2 x

Vereinfache

\frac{3}{4} \cdot \frac{2}{3 ( x ^{2} - 1 ) ^{\frac{1}{3}}} \cdot 2 x : \frac{x}{( x ^{2} - 1 ) ^{\frac{1}{3}}}

= \frac{x}{( x ^{2} - 1 ) ^{\frac{1}{3}}}

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