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Beliebt Rechnen >

derivative f(x)=\sqrt[3]{(x-4)^2}

Lösung

ableitung von

f (x) = 3 (x - 4)^{2}

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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