derivative f(x)=(3x^4+8)^{4/3}

Lösung

ableitung von

f (x) = (3 x^{4} + 8)^{\frac{4}{3}}

16 x^{3} (3 x^{4} + 8)^{\frac{1}{3}}

Schritte zur Lösung

\frac{d}{d x} ((3 x^{4} + 8)^{\frac{4}{3}})

Wende die Kettenregel an:

\frac{4 ( 3 x ^{4} + 8 ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (3 x^{4} + 8)

= \frac{4 ( 3 x ^{4} + 8 ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (3 x^{4} + 8)

\frac{d}{d x} (3 x^{4} + 8) = 12 x^{3}

= \frac{4 ( 3 x ^{4} + 8 ) ^{\frac{1}{3}}}{3} \cdot 12 x^{3}

Vereinfache

\frac{4 ( 3 x ^{4} + 8 ) ^{\frac{1}{3}}}{3} \cdot 12 x^{3} : 16 x^{3} (3 x^{4} + 8)^{\frac{1}{3}}

= 16 x^{3} (3 x^{4} + 8)^{\frac{1}{3}}

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